Miryam Ghorashy obtained a $1,500 loan at an interest rate of 10%. The monthly payment is $131.85. What is the new principal after the first payment?

Answer:

The new principal after the first payment is $1380.65.

Step-by-step explanation

First, determine the Effective annual interest rate 

Effective annual interest rate = (1 + (nominal rate / number of compounding periods)) ^{(number of compounding periods)} - 1

Effective annual interest rate = (1+(0.10/12))¹² - 1

Effective annual interest rate = 0.104713 = 10.4713%

Then, calculate the present value of the first payment,

FV = PV(1+r)ⁿ

PV = FV/ (1+r)ⁿ

PV = $131.85 / (1+0.104713)¹

PV = $119.3522

Lastly, determine the new principal after the first payment,

New principal = $1500 - $119.3522

New principal = $1380.6478