Question

Exercies 7: Reem took out a 20-year lon of 200,000 that she will pay off with quarterly payments. With the 40th payment, she will add an extra 20,000. She will make level quarterly payment of , starting from 3-months from the original loan date. Reem will pay off the loan exactly with the last full payment of Calculate at an interest rate of 8% convertible quarterly.

Answer 1

There are a total of 20years*4 = 80 quarterly payments

Value of the loan today = 200,000

Extra 20,000 is deposited at 40th payment ie. at the 40th quarter ie. just after 10 years

PV of the extra 20,000 deposited after 40th payment (10 years) = 20000/((1+0.08/4)^40) = $9057.81

Value of the loan today after considering the extra 20,000 payment = $200,000-$9057.81 = $190,942.19

Hence, the problem reduces to what will be the quarterly payment X, if the PV of loan is $190,942.19 at rate of 8% compounded quarterly

We use a financial calculator

PV = -190,942.19

FV = 0

I/Y = 8%/4 = 2%

N = 20*4 = 80

CPT PMT, we get

PMT = 4804.24

Hence X = $4804.24