Question

Question 12 (1 point) Charles just borrowed $3,565.00 and agreed to repay it with three equal payments. The first will be in 2 months, the second in 4 months and the third in 6 months Usin g a simple interest rate of 5.25% per annum, calculate the size of each payment. today as the focal date and express your answer to 2 decimal places Use Your Answer Answer

Answer 1

We have following information -

Borrowed Amount = $ 3,565

Simple interest rate = 5.25% pa

thus, Simple interest rate for a month = 0.0525/12 = 0.004375

Repayment = 3 equal payment in 2nd, 4th & 6th month.

Let's assume repayment value is $ X

The Present value(PV) of all three equal payment at simple interest should be equal to Borrowed amount today.

Thus,

Borrowed Amount = PV of repayments

$Borrowed amount =\sum_{n=1}^{n} \frac{Repayment}{1+rt}$$3565 =\frac{X}{1+(0.004375*2)} +\frac{X}{1+(0.004375*4)}+\frac{X}{1+(0.004375*6)}$

$3565 =\frac{X}{1.00875} +\frac{X}{1.0175}+\frac{X}{1.02625}$

$3565 = X \left ( \frac{1}{1.00875} +\frac{1}{1.0175}+\frac{1}{1.02625} \right )$

$3565 = X \left ( 0.9913 + 0.9828+0.9744 \right )$

$3565 = X \left ( 2.9485 \right )$

$X =\frac{3565}{2.9485}$

$X = 1209.09$

Thus, the equal repayment is $ 1209.09

Please note - PV of equal repayment is calculated based on Simple interest factor.