Question

A loan of $19,221 was repaid at the end of 17 months. What size repayment check (principal and interest) was written, if a 9.7% annual rate of interest was charged? The amount of the repayment check was $ 45447.53). (Round to two decimal places.)

Answer 1

The size of the repayment check is $21,868.50.

Explanation:

The repayment check is going to be:

R = Principal + Interest

The principal is $19,221. We have to find the value of the interest.

The interest can be calculated as simple interest, given by the following formula:

`I = P*r*t`

In which P is the principal, r is the annual interest rate, in decimal, and t is the time, in years.

In this problem, we have that:

`P = 19,221`,
`r = 0.097`

The time is 17 months. However, we must convert this value to years. Each year has 12 months. So 17 months is
`(17)/(12) = 1.42` years. So
`t = 1.42`

The interest value is:

`I = P*r*t`

`I = 19,221*0.097*1.42`

`I = 2647,50`

The size of the repayment check is:

R = Principal + Interest

`R = P + I`

`R = 19,221 + 2647,50`

`R = 21,868.50`

The size of the repayment check is $21,868.50.