Question

Suppose that a loan is being repaid with 60 equal monthly payments, the first coming a month after the loan is made. If the rate of interest is 7.5 percent convertible monthly, and the amount of principal in the 22nd payment is 210, how much interest is in the 44th payment?

Answer 1

We have following formula to calculate nth principal payment

Principal paid (nth payment) = Total monthly Payment / [1+R) ^ (N-n+1)]

Where,

Principal paid (22th payment) = $210

Total monthly Payment =?

Monthly interest rate (R) = 7.5%/12 = 0.625%

Total number of payments (N) = 60

Payment for with principal amount is known (n) = 22

Therefore,

$210 = Total monthly Payment/ [1+0.625%) ^ (60-22+1)]

Or Total monthly Payment = $210 * [1+0.625%) ^ (60-22+1)]

= $210 * 1.275

= $267.76

Now to calculate interest is in the 44th payment; first we have to calculate Principal paid (44th payment)

Principal paid (44th payment) = Total monthly Payment/ [1+0.625%) ^ (60-44+1)]

=$267.76/1.112 = $240.85

But total monthly payment is $267.76

Therefore, interest is in the 44th payment = total monthly payment - Principal paid (44th payment)

=$267.76 -$240.85

= $26.91

Interest is in the 44th payment is $26.91