# APR for a Loan Paid Off Monthly

A loan is issued for 12 months for 1000 and is paid back with monthly payments of \$140 each month. Does this loan have an APR of 68%?

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. 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%

• Good point; I was very sloppy, ignoring the payoff of principal along the way. – keshlam Nov 19 '14 at 3:32
• In the US, isn't the APR defined in the Truth in Lending Act as the periodic rate times the number of times compounding is done each year and so the APR is 108.6%? Is it the Effective Annual Percentage Rate (EAPR) as defined in the European Union which is 182.8%? – Dilip Sarwate Nov 19 '14 at 3:33
• @JoeTaxpayer Sorry, it looks to me like you're assuming compounding. Isn't this not being compounded? – user22347 Nov 25 '14 at 17:58
• The 108% has no impact from compounding. – JTP - Apologise to Monica Nov 25 '14 at 18:31
• @Joe Sorry, where did you get the 9.05 from? – user22347 Nov 25 '14 at 23:35

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