APR for a Loan Paid Off Monthly
The periodic rate (here, the interest charged per month), as you would enter into a finance calculator is 9.05%. Multiply by 12 to get 108.6% or calculate APR at 182.8%. Either way it's far more than 68%.  If the $1680 were paid after 365 days, it would be simple interest of 68%. For the fact that payment are made along the way, the numbers change.  Edit - A finance calculator has 5 buttons to cover the calculations:  N = number of periods or payments %i = the interest per period PV = present value PMT = Payment per period FV= Future value In your example, you've given us the number of periods, 12, present value, $1000, future value, 0, and payment, $140. The calculator tells me this is a monthly rate of 9%. As Dilip noted, you can compound as you wish, depending on what you are looking for, but the 9% isn't an opinion, it's the math. TI BA-35 Solar. Discontinued, but available on eBay. Worth every cent.  Per mhoran's comment, I'll add the spreadsheet version.  I literally copied and pasted his text into a open cell, and after entering the cell shows,  which I rounded to 9.05%. Note, the $1000 is negative, it starts as an amount owed.  And for Dilip - 1.0905^12 = 2.8281 or 182.8% effective rate. If I am the loanshark lending this money, charging 9% per month, my $1000 investment returns $2828 by the end of the year, assuming, of course, that the payment is reinvested immediately. The 108 >> 182 seems disturbing, but for lower numbers, even 12% per year, the monthly compounding only results in 12.68% If your APR is quoted as nominal rate compounded monthly, the APR is 108.6 %. Here is the calculation, (done in Mathematica ). The sum of the discounted future payments (p) are set equal to the present value (pv) of the loan, and solved for the periodic interest rate (r).  Details of the effective interest rate calculation can be found here. http://en.wikipedia.org/wiki/Effective_interest_rate#Calculation
There are a few ways to look at this question. Assumptions. Per the original post's assumptions, this answer: In other words, if the owner paid the mortgage on its original schedule, the deal could boil down to a $ 40,000 up-front payment, in exchange for $ 200,000 of equity after 30 years.  Or the deal could boil down to a $ 40,000 up-front payment, in exchange for a $ 810.70 monthly payment starting in 30 years. While the owner is paying down the mortgage, the return on equity is the principal payment divided by the equity.  The principal payment is the net rent minus non-financing costs and interest, so it is actually a profit. The initial return on equity is 6.321 % APR, or 6.507 % APY.  This is calculated by dividing the $ 210.70 monthly principal payment by the initial $ 40,000 equity, and converting from monthly return to annual return. After 30 years, the return on equity is 4.864 % APR, or 4.974 % APY.  This is calculated by dividing the $ 810.70 monthly cash flow (which is no longer reduced by mortgage payments) by the $ 200,000 equity after 30 years, and converting from monthly return to annual return. The cap rate is the same as the return on equity in the absence of debt.  In this example, 4.864 % APR, or 4.974 % APY. The return on equity declines from 6.507 % APY initially to 4.974 % APY after 30 years. This is because the cap rate exceeds the note rate (4.974 % APY vs. 4.594 % APY), and the leverage decreases from 5x to 1x. The weighted average compound annual growth rate of the equity during the 30 years is 5.511 % APY.  Per the original poster's answer, this is computed by taking the 30th root of the 5-fold increase in equity.  Because the owner made no extra principal payments (besides those already discussed), the relevant amounts are the initial $ 40,000 owner payment and the final $ 200,000 owner equity.  5.511 % APY corresponds to a 5.377 % APR. The internal rate of return if the owner never sells can be computed by treating the deal as a $ 40,000 up-front payment, in exchange for an $ 810.70 monthly payment starting in 30 years.  The internal rate of return (IRR) is not a very useful number, because it assumes that you can somehow reinvest the eventual dividends at the same rate.  In this example, the IRR is 5.172 % APR, or 5.296  % APY.  In this example, the IRR is calculated by (iteratively) finding an interest rate for which (initial investment) * (1 + IRR) ^ (number periods before dividends start) = (periodic dividend) / (IRR - growth rate of dividend).  For example: $ 40,000 * (1.004309687)^360 = $ 810.70 / (0.004309687 - 0) = $ 188,111 I then converted the 0.431 % monthly IRR to an annual IRR. The deal can be thought of as a return on equity, plus a return on paying down the mortgage. When computing the return from paying down the mortgage, the initial equity is irrelevant.  It does not matter whether you start with a $ 160,000 mortgage on a $ 160,000 property, a $ 160,000 mortgage on a $ 200,000 property, or a $ 160,000 mortgage on a $ 1,000,000 property.  All that matters is the note rate on the mortgage, which is the applicable compound interest rate. The return on paying down the mortgage equals the note rate of the mortgage.  For a 4.5% note rate, this works out to a 4.594% annual percentage yield (APY). You can confirm this by looking at your amortization schedule.  Suppose you have a $ 160,000 mortgage with a fixed 4.5% APR note rate for 360 months.  Your monthly payment is $ 810.70.  In the first month, $ 600 goes toward interest, and $ 210.70 reduces the principal.  In other words, the $ 210.70 principal payment eliminated the need for a $ 810.70 payment 30 years later.  Notice that: . $ 210.70 * (1 + 0.045 / 12)^360 = $ 210.70 * (1.00375)^360 = $ 210.70 * 3.8477 = $ 810.71 which is within rounding error of $ 810.70. The interest rate is 3/8 % per month, which is an APR of 4.5%, and an APY of 4.594 %. Generally, I would say that you should pay it off if you have the money available. Why pay interest if you have the money? That is, of course, if your money can earn you more than the interest you pay (which can happen if you got a very low APR for your car loan, but then you probably have excellent credit already and shouldn't care about the history of the loan on your report). Re the 7 years vs 2 years - to the best of my knowledge its not true, it will stay 7 years even if its closed during the first year. If you keep the monthly payment the same, and the interest is lower; then you will be by definition overpaying the new loan therefore it will be paid off sooner. Based on some quick calculations it will be paid off approximately 5 years sooner. One advantage to the new loan is that you will have flexibility, you can drop the payment to the lower level for a few months because of a big financial problem and not be in default. Withdrawing from your 401(k) may include a 10% withdrawal penalty. There are ways to avoid the withdrawal penalty for early disbursements. The idea is to reduce your interest expense by leveraging free loans (0% APR purchases). This will help you pay down your debt more.  If you have 0% APR on purchases, you can make purchases on things you already buy. Then use that money towards other debt, while making monthly payments on the 0% APR card. This way, you pay off the credit card before the 0% APR changes. You can then rinse and repeat on another 0% APR card offer. If your credit score is 800, you can do this multiple times. Citi Simplicity gives you 18 months 0% APR. Chase Slate and Chase Freedom gives you 15 months 0% APR. Others typically give you 12 months or less. Is the pay cycle every 2 weeks? So 30% each two week period is 1.3^26 = 917.33 or an APR of 91633%.  Loansharks charge less, I believe standard vig was 2%/week for good customers. Only 180% per year. This is what your car loan would look like if you paid it off in 14 months at the existing 2.94% rate: You'll pay a total of about $277 in interest.   If you do a balance transfer of the $10,000 at 3% it'll cost you $300 up front, and your payment on the remaining $5,000 will be $363.74 to pay it off in the 14 month period.  Your total monthly payment will be $1,099.45; $5,000 amortized at 2.94% for 14 months plus $10,300 divided by 14. ($363.74 + 735.71).  Your interest will be about $392, $300 from the balance transfer and $92 from the remaining $5,000 on the car loan at 2.94%. Even if your lender doesn't credit your additional payment to principal and instead simply credits future payments, you'd still be done in 15 months with a total interest expense of about $447.  So this additional administration and additional loan will save you maybe about $55 over 14 or 15 months. "Check out the Mortgage Professor's website, in particular Calculator 11a: Who This Calculator is For: Borrowers who want to know whether they   will save or lose money over a specified period by paying points in order   to reduce the interest rate on an FRM. What This Calculator Does:This calculator shows the costs and benefits   of paying points to reduce the rate on an FRM, and the minimum period   they must hold an FRM before it makes sense to pay   additional points (the ""break-even period"")." If I recall correctly, the pay schedule is such that you initially pay mostly interest.  As James Roth suggests, look at the terms of the loan, specifically the payment schedule.  It should detail how much is being applied to interest and how much to the actual balance.