Question

You take out a loan for $4000 at an annual interest rate of 5% (compounded annually). You must pay back the loan in 3 annual installments. How much of the principal is still outstanding after you make the first payment? g

Answer 1

Answer: = $2,731.14

Explanation:

First find the annual payment.

The payment will be constant so is an annuity.

Present Value of an Annuity = Payment * Present Value Interest Factor of an annuity

4,000 = Payment * PVIFA( 3 periods, 5%)

4,000 = Payment * 2.7232

Payment = 4,000 / 2.7232

Payment = $1,468.86

This annual Payment is divided into an interest component and a component going towards principal repayment.

Interest component =  5% * 4,000

= $200

Amount going to principal = 1,468.86 - 200

= $1,268.86

Amount of Principal Outstanding = 4,000 - 1,268.86

= $2,731.14