What does 30 percent APR on a 1200 dollar purchase mean if you intend on paying off the entire expense within 4 months which is well before a years time?

Answer 1

APR is annual percentage rate. This should be the rate you would expect if the amount was held for a full year.

However, interest is usually accrued on a monthly basis, in which case, the interest rate would be:

monthly_percentage_rate = ((1 + APR/100)1/12 - 1) x 100

(as compound, not simple interest is used - the interest that is not paid off is added to your loan for the next month's interest calculation). So for 30%APR, the Monthly Percentage Rate would be ((1 + 30/100)1/12 - 1) x 100 ~= 2.21%

If you were going to pay off a loan at the end of 4 months, the percentage rate you would pay would be ((1 + 2.21/100)4 - 1) x 100 ~= 9.139%, that is if you borrowed $1200, you would have to pay back $1309.67 at the end of 4 months, but if you had it for the full year, you would have to pay back $1560.

But you often pay back in monthly instalments, in which case you will (should) be paying off interest and part of the capital each month, the proportion of the payment that is capital rising with each payment), so the amount you pay back each month should be calculated by:

Monthly_repayment = loan x (mrn x (mr - 1) / (mrn - 1))

where mr = monthly_rate is calculated as (1 + apr / 100)1/12, and n is the number of months.

So for $1200 loan at 30% apr for 4 months, the monthly repayment would be:

mr = (1 + 30/100)1/12 ~= 1.0221

Monthly_repayment = $1200 x (1.02214 x 0.0221 / (1.02214 - 1)

~= $316.76

making a total repayment for the 4 months of $1267.04

Over a whole year, n = 12, monthly_repayment ~= $114.94, total repayment = £1379.32 which is just under half the interest you would pay if it was all paid back at the end of the year.