Car finance, APR rates and per week in adverts; help understanding them
Easier to copy paste than type this out. Credit: www.financeformulas.net Note that the present value would be the initial loan amount, which is likely the sale price you noted minus a down payment.   The loan payment formula is used to calculate the payments on a loan.   The formula used to calculate loan payments is exactly the same as the   formula used to calculate payments on an ordinary annuity. A loan, by   definition, is an annuity, in that it consists of a series of future   periodic payments. The PV, or present value, portion of the loan payment formula uses the   original loan amount. The original loan amount is essentially the   present value of the future payments on the loan, much like the   present value of an annuity. It is important to keep the rate per period and number of periods   consistent with one another in the formula. If the loan payments are   made monthly, then the rate per period needs to be adjusted to the   monthly rate and the number of periods would be the number of months   on the loan. If payments are quarterly, the terms of the loan payment   formula would be adjusted accordingly. I like to let loan calculators do the heavy lifting for me. This particular calculator lets you choose a weekly pay back scheme. http://www.calculator.net/loan-calculator.html "Taking the last case first, this works out exactly. (Note the Bank of England interest rate has nothing to do with the calculation.) The standard loan formula for an ordinary annuity can be used (as described by BobbyScon), but the periodic interest rate has to be calculated from an effective APR, not a nominal rate.  For details, see APR in the EU and UK, where the definition is only valid for effective APR, as shown below. 2003 BMW 325i £7477 TYPICAL APR 12.9% 60 monthly payments £167.05 How does this work? See the section Calculating the Present Value of an Ordinary Annuity.  The payment formula is derived from the sum of the payments, each discounted to present value. I.e. The example relates to the EU APR definition like so.  Next, the second case doesn't make much sense (unless there is a downpayment). 2004 HONDA CIVIC 1.6 i-VTEC SE 5 door Hatchback £6,999 £113.15 per month ""At APR 9.9% [as quoted in advert], 58 monthly payments"" 58 monthly payments at 9.9% only amount to £5248.75 which is £1750.25 less than the price of the car. Finally, the first case is approximate. 2005 TOYOTA COROLLA 1.4 VVTi 5 door hatchback £7195 From £38 per week ""16.1% APR typical, a 60 month payment, 260 weekly payments"" A weekly payment of £38 would imply an APR of 14.3%."
"Short answer:  No. Longer answer:  The only reason to move would be to get out of the condo and into a SFR of equal cost because condos can be quite difficult to sell and you don't really want that potential burden later on.  Moving is expensive though and you can't afford to spend more when you are already living on the financial edge. Speaking of living on the edge, that's a recipe for disaster.  I make, ratio-wise, a similar sort of income.  Even accounting for the generous college tuition, you should be able to save at least $20K per year...at a bare minimum.  And if you were careful, I figure you should be able to save $40K/year.  You need to figure out where you are dumping all of your money and cut WAY back on spending and focus entirely on saving money. 1)  Stop eating out.  Make your own meals.  I average about $2 per meal per person - no junk food.  Eating out is 6 to 30 times as expensive as making meals at home.  Do the math:  $10 * 2 people * number of times you eat out per week * 52 ($1,040 per year for each time/week!) vs $2 * 2 people * 21 (3 meals per day) * 52 ($4,368 per year for both of you...maximum).  Now I know some meals are more expensive to prepare, but the math is not unrealistic - I spend about $140 per month on groceries and make the bulk of my own food.  Eating out is sticker shock for me.  The food I prepare is nutritionally balanced and complete.  Now I'm not a complete health-nut.  I love the occasional deep-fried treat or hamburger, but those are ""once every couple of months"" sort of things, which makes them special. 2)  Stop going to Starbucks or wherever you habitually go.  It takes fuel to get there.  It's also expensive when you get there.  Bring your own drink if you are hanging out with friends. 3)  Drop golf.  Or whatever expensive sport you are sinking money into.  Invest in some cheap running clothes and focus on cardio-based workouts.  Heart health is more important than anything else.  If you can't live without your sport, then find an alternate sport that is ""equal""-ish in challenge but a ton cheaper to play.  For example, if you like playing golf, play discgolf instead (most cities have courses) - there's no cost beyond a couple of discs and the challenge is still there. 4)  Drop entertainment.  Movies at the theater are expensive.  Drop your cable subscription (you are getting financially raped for $1,500/year).  Get a Netflix subscription and find shows via free online streaming services.  Buy some dominoes, card games, and a couple of classic board games.  Keep entertainment simple and cheap. 5)  Drop your cell phone's data plan.  Republic Wireless is the only decent cellular provider and even their $12/month plan is living a luxury lifestyle.  If you spend more than $10/month/person for phone service, you are spending too much. 6)  Stop driving everywhere.  Gas is expensive.  Cars are expensive.  If you have more than two cars, sell the extras.  If your car is worth more than $20,000, sell it and get something cheaper. 7)  Stop drinking alcohol.  Alcohol impairs mental functions, is addictive, smells terrible, and is ridiculously expensive.  There's no actual need to consume it either. By the way, don't go and make major financial changes without the wife's sign-off.  Finances are the #1 reason for divorce.  So get her ""OK"" on this stuff.  Hopefully you already knew that.  The above are just some common financial pitfalls where people sink thousands and thousand of dollars and gain nothing.  You can still have a full and complete life with just a minimum of the above. There is no excuse for living on the edge financially.  Your story is one I'm going to share with those who give me the same excuse because they are ""poor"".  You are ""I want to punch you in the face"" wealthy and you spend every last penny because you think that's how money works.  You are wrong. One final piece of advice:  Find a financial adviser.  It is clear to me that you've been managing money wrong your whole life.  A financial adviser will look at your situation and help you far more than someone on the Internet ever can.  If you attend a church, many churches have the excellent Crown Financial Ministries program available which teaches sound financial management principles.  The education system doesn't show people how to manage money, but that's not an excuse either.  Once you dig yourself out of the financial hole you've dug for yourself, you can pass the knowledge on how to correctly manage money onto other people." "Basically, the easiest way to do this is to chart out the ""what-ifs"". Applying the amortization formula (see here) using the numbers you supplied and a little guesswork, I calculated an interest rate of 3.75% (which is good) and that you've already made 17 semi-monthly payments (8 and a half months' worth) of $680.04, out of a 30-year, 720-payment loan term. These are the numbers I will use. Let's now suppose that tomorrow, you found $100 extra every two weeks in your budget, and decided to put it toward your mortgage starting with the next payment. That makes the semi-monthly payments $780 each. You would pay off the mortgage in 23 years (making 557 more payments instead of 703 more). Your total payments will be $434,460, down from $478.040, so your interest costs on the loan were reduced by $43,580 (but, my mistake, we can't count this amount as money in the bank; it's included in the next amount of money to come in). Now, after the mortgage is paid off, you have $780 semi-monthly for the remaining 73 months of your original 30-year loan (a total of $113,880) which you can now do something else with. If you stuffed it in your mattress, you'd earn 0% and so that's the worst-case scenario. For anything else to be worth it, you must be getting a rate of return such that $100 payments, 24 times a year for a total of 703 payments must equal $113,880. We use the future value annuity formula (here): v = p*((i+1)n-1)/i, plugging in v ($113880, our FV goal), $100 for P (the monthly payment) and 703 for n (total number of payments. We're looking for i, the interest rate. We're making 24 payments per year, so the value of i we find will be 1/24 of the stated annual interest rate of any account you put it into. We find that in order to make the same amount of money on an annuity that you save by paying off the loan, the interest rate on the account must average 3.07%. However, you're probably not going to stuff the savings from the mortgage in your mattress and sleep on it for 6 years. What if you invest it, in the same security you're considering now? That would be 146 payments of $780 into an interest-bearing account, plus the interest savings. Now, the interest rate on the security must be greater, because you're not only saving money on the mortgage, you're making money on the savings. Assuming the annuity APR stays the same now vs later, we find that the APR on the annuity must equal, surprise, 3.75% in order to end up with the same amount of money. Why is that? Well, the interest growing on your $100 semi-monthly exactly offsets the interest you would save on the mortgage by reducing the principal by $100. Both the loan balance you would remove and the annuity balance you increase would accrue the same interest over the same time if they had the same rate. The main difference, to you, is that by paying into the annuity now, you have cash now; by paying into the mortgage now, you don't have money now, but you have WAY more money later. The actual real time-values of the money, however, are the same; the future value of $200/mo for 30 years is equal to $0/mo for 24 years and then $1560/mo for 6 years, but the real money paid in over 30 years is $72,000 vs $112,320. That kind of math is why analysts encourage people to start retirement saving early. One more thing. If you live in the United States, the interest charges on your mortgage are tax-deductible. So, that $43,580 you saved by paying down the mortgage? Take 25% of it and throw it away as taxes (assuming you're in the most common wage-earner tax bracket). That's $10895 in potential tax savings that you don't get over the life of the loan. If you penalize the ""pay-off-early"" track by subtracting those extra taxes, you find that the break-even APR on the annuity account is about 3.095%." "By the sounds of things, you're not asking for a single formula but how to do the analysis... And for the record you're focusing on the wrong thing. You should be focusing on how much it costs to own your car during that time period, not your total equity.  Formulas:  I'm not sure how well you understand the nuts and bolts of the finance behind your question, (you may just be a pro and really want a consolidated equation to do this in one go.) So at the risk of over-specifying, I'll err on the side of starting at the very beginning. Any financial loan analysis is built on 5 items: (1) # of periods, (2) Present Value, (3) Future Value, (4) Payments, and (5) interest rate.  These are usually referred to in spreadsheet software as NPER, PV, FV, PMT, and Rate. Each one has its own Excel/google docs function where you can calculate one as a function of the other 4. I'll use those going forward and spare you the 'real math' equations.  Layout: If I were trying to solve your problem I would start by setting up the spreadsheet  up with column A as ""Period"". I would put this label in cell A2 and then starting from cell A3 as ""0"" and going to ""N"". 5 year loans will give you the highest purchase value w lowest payments, so n=60 months... but you also said 48 months so do whatever you want.  Then I would set up two tables side-by-side with 7 columns each. (Yes, seven.) Starting in C2, label the cells/columns as: ""Rate"", ""Car Value"", ""Loan Balance"", ""Payment"", ""Paid to Interest"", ""Principal"", and ""Accumulated Equity"". Then select and copy cells C2:I2 as the next set of column headers beginning in K2. (I usually skip a column to leave space because I'm OCD like that :) ) Numbers: Now you need to set up your initial set of numbers for each table. We'll do the older car in the left hand table and the newer one on the right. Let's say your rate is 5% APR. Put that in cell C1 (not C3). Then in cell C3 type =C$1/12. Car Value $12,000 in Cell D3. Then type ""Down Payment"" in cell E1 and put 10% in cell D1. And last, in cell E3 put the formula =D3*(1-D$1). This should leave you with a value for the first month in the Rate, Car Value, and Loan Balance columns. Now select C1:E3 and paste those to the right hand table. The only thing you will need to change is the ""Car Value"" to $20,000. As a check, you should have .0042 / 12,000 / 10,800 on the left and then .0042 / 20,000 / 18,000 on the right.  Formulas again: This is where spreadsheets become amazing. If we set up the right formulas, you can copy and paste them and do this very complicated analysis very quickly.  Payment The excel formula for Payment is =PMT(Rate, NPER, PV, FV). FV is usually zero. So in cell F3, type the formula =PMT(C3, 60, E3, 0). Obviously if you're really doing a 48 month (4 year) loan then you'll need to change the 60 to 48. You should be able to copy the result from cell F3 to N3 and the formula will update itself.  For the 60 months, I'm showing the 12K car/10.8K loan has a pmt of $203.81. The 20K/18K loan has a pmt of 339.68.  Interest The easiest way to calculate the interest is as =E3*C3. That's (Outstanding Loan Balance) x (Periodic Interest Rate). Put this in cell G4, since you don't actually owe any interest at Period 0.  Principal If you pay PMT each month and X goes to interest, then the amount to principal is ""PMT - X"". So in H4 type =-F3 - G3. The 'minus' in front of F3 is because excel's PMT function returns a negative amount. If you want to, feel free to type ""=-PMT(...)"" for the formula that's actually in F3. It's your call.  I get 159 for the amount to principal in period 1.  Accumulated Equity As I mentioned in the comment, your ""Equity"" comes from your initial Loan-to-Value and the accumulated principal payments. So the formula in this cell should reflect that. There are a variety of ways to do this... the easiest is just to compare your car's expected value to your loan balance every time. In cell I3, type =(D3-E3). That's your initial equity in the car before making any payments. Copy that cell and paste it to I4. You'll see it updates to =(D4-E3) automatically. (Right now that is zero... those cells are empty, but we're getting there) The important thing is that as JB King pointed out, your equity is a function of accumulated principal AND equity, which depreciates. This approach handles those both.  Finishing up the copy-and-paste formulas I know this is long, but we're almost done.  Rate // Period 1 In cell C4 type =C3.  Payment // Period 1 In cell F4 type =F3.  Loan Balance // Period 1 In cell E4 type =E3-H4. Your loan balance at the end of period is reduced by the principal you paid. I get 10,641.  Car Value // Period 1 This will vary depending on how you want to handle depreciation. If you ignore it, you're making a major error and it's not worth doing this entire analysis...  just buy the prettiest car and move on with life. But you also don't have to get it scientifically accurate. Go to someplace like edmunds.com and look up a ballpark. I'm using 4% depreciation per year for the old (12K) car and 7% for the newer car. However, I pulled those out of my ass so figure out what's a better ballpark.  In G1 type ""Depreciation"" and then put 4% in H1. In O1 type ""Depreciation"" and then 7% in P1. Now, in cell D4, put the formula =D3 * (1-(H$1/12)).  Paste formulas to flesh out table As a check, your row 4 should read 1 / .0042 / 11,960 / 10,641 / 203.81 / 45 / 159 / 1,319. If so, you're great. Copy cells C4:I4 and paste them into K4:Q4.  These will update to be .0042 / 19,883 / 17,735 / 339.68 / 75 / 265 / 2,148.  If you've got that, then copy C4:Q4 and paste it to C5:C63. You've built a full amortization table for your two hypothetical loans. Congratulations.  Making your decision I'm not going to tell you what to decide, but I'll give you a better idea of what to look at. I would personally make the decision based on total cost to own during that time period, plus a bit of ""x-factor"" for which car I really liked.  Look at Period 24, in columns I and Q. These are your 'equities' in each car. If you built the sheet using my made-up numbers, then you get ""Old Car Equity"" as 4,276. ""New Car Equity"" is 6,046. If you're only looking at most equity, you might make a poor financial decision.  The real value you should consider is the cost to own the car (not necessarily operate it) during that time... Total Cost = (Ending Equity) - (Payment x 24) - (Upfront Cash).  For your 'old' car, that's (4,276) - (203.81 * 24) - (1,200) = -1,815.75 For the 'new' car, that's (6,046) - (339.68 * 24) - (2,000) = -4,106.07.  Is one good or bad? Up to you to decide. There are excel formulas like ""CUMPRINC"" that can consolidate some of the table mechanics, but I assumed that if you're here asking you would have gotten stuck running some of those.  Here's the spreadsheet: https://docs.google.com/spreadsheet/ccc?key=0Ah0weE0QX65vdHpCNVpwUzlfYjlTY2VrNllXOS1CWUE#gid=1" Generally speaking personal loans have higher rates than car loans.  During fairly recent times, the market for car loans has become very competitive.  A local credit union offers loans as low as 1.99% which is about half the prevailing mortgage rate.  In comparison personal loans are typically in the 10-14% range.   Even if it made mathematical sense to do so, I doubt any bank would give you a personal loan secured by a car rather than car loan.  Either the brain would not work that way; or, it would simply be against company policy. These questions always interest me, why the desire to maximize credit score?  There is no correlation between credit score and wealth.  There is no reward for anything beyond a sufficiently high score to obtain the lowest rates which is attained by simply paying one's bills on time.  One will always be limited by income when the amount able to borrow is calculated regardless of score.   I can understand wanting to maximize different aspects of personal finance such as income or investment return percentage, etc..  By why credit score?  This is further complicated by a evolving algorithm.  Attempts to game the score today, may not work in the future. In the U.S., most car dealers provide lease financing through one company (usually a subsidiary of the auto manufacturer). Whereas they provide loan financing through a variety of companies, some of whom offer very high interest rate loans and sell the loans as collateralized debt obligations (CDOs). Have you checked whether Chase or First Tech Credit Union offers a suitable car lease? There needs to be more numbers with your choices, without those any answer is purely speculation. Assuming that India is much like the US, you are almost always better to go with a company leased car.  That is if you are not responsible for the lease if your employment ends with the company. Here in the US companies typically reimburse, so tax free, their employees for about 50 cents per mile, or about 31 cents per kilometer.  This barely covers the gas and insurance and falls way short when one includes deprecation and maintenance.  So it is better to have the company to pick up all those costs.      Borrowing money on a car is just plain dumb no matter what the interest rate.  So I would stick with choice number 1 or 3 depending on the arrangement for the company leased car. The next question becomes how much you should spend for a car?  I would say enough to keep you happy and safe, but not much more than that until you are wealthy. "I'm going to ignore your numbers to avoid spending the time to understand them.  I'm just going to go over the basic moving parts of trading an upside down car against another financed car because I think you're conflating price and value.  I'm also going to ignore taxes, and fees, and depreciation. The car has an acquisition cost (price) then it has a value.  You pay the price to obtain this thing, then in the future it is worth what someone else will pay you. When you finance a car you agree to your $10,000 price, then you call up Mr. Bank and agree to pay 10% per year for 5 years on that $10,000.  Mr. Banker wires over $10,000 and you drive home in your car.   Say in a year you want a different car.  This new car has a price of $20,000, and wouldn't you know it they'll even buy your current car from you.  They'll give you $7,000 to trade in your current car. Your current car has a value of $7,000.  You've made 12 payments of $188.71.  Of those payments about $460 was interest, you now owe about $8,195 to Mr. Banker. The new dealership needs to send payment to Mr. Banker to get the title for your current car.  They'll send the $7,000 they agreed to pay for your car.  Then they'll loan you the additional $1,195 ($8,195 owed on the car minus $7,000 trade in value).   Your loan on the new car will be for $21,195, $20,000 for the new car and $1,195 for the amount you still owed on the old car after the dealership paid you $7,000 for your old car. It doesn't matter what your down-payment was on the old car, it doesn't matter what your payment was before, it doesn't matter what you bought your old car for.  All that matters is how much you owe on it today and how much the buyer (the dealership) is willing to pay you for it. How much of this is ""loss"" is an extremely vague number to derive primarily because your utility of the car has a value.  But it could be argued that the $1,195 added on to your new car loan to pay for the old car is lost." Unless you are getting the loan from a loan shark, it is the most common case that each payment is applied to the interest accrued to date and the rest is applied towards reducing the principal.  So, assuming that fortnightly means 26 equally-spaced payments during the year, the interest accrued at the end of the first fortnight is $660,000 x (0.0575/26) = $1459.62 and so the principal is reduced by $2299.61 - $1459.62 = $839.99 For the next payment, the principal still owing at the beginning of that fortnight will be $660,000-$839.99 = $659,160.01 and the interest accrued will be $659,160.01 x (0.0575/26) = $1457.76 and so slightly more of the principal will be reduced than the $839.99 of the previous payment.  Lather, rinse, repeat until the loan is paid off which should occur at the end of 17.5 years (or after 455 biweekly payments). If the loan rate changes during this time (since you say that this is a variable-rate loan), the numbers quoted above will change too. And no, it is not the case that just %5.75 of the $2300 is interest, and the rest comes off the principle (sic)? Interest is computed on the principal amount still owed ($660,000 for starters and then decreasing fortnightly). not the loan payment amount. Edit  After playing around with a spreadsheet a bit, I found that if  payments are made every two weeks (14 days apart) rather than 26 equally spaced payments in one year as I used above, interest accrues at the rate of 5.75 x (14/365)% for the 14 days rather than at the rate of (5.75/26)% for the time between payments as I used above each 14 days, $2299.56 is paid as the biweekly mortgage payment instead of the $2299.61 stated by the OP, then 455 payments (slightly less than 17.5 calendar years when leap years are taken into account) will pay off the loan.  In fact, that 455-th payment should be reduced by 65 cents.  In view of rounding of fractional cents and the like, I doubt that it would be possible to have the last equal payment reduce the balance to exactly 0.