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

Answer:

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

Step-by-step 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 $\frac{17}{12} = 1.42$ 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.