Question

You take out a 40 year loan with effective annual interest i = .05 and yearly payments at the end of each year being $10, 000 for the first 20 years, and then $15, 000 for the next 20 years. Find the outstanding balance after the fourth payment. Also find the outstanding balance after the 37th payment.

Answer 1

Loan amount is the sum of (a) PV of annuity of $10,000 for 20 payments and (b) Discounted value (PV) of PV of another annuity of $15,000 for next 20 years.

Given, interest rate= 5%

Therefore, Loan amount= $10,000*PVA(5%,20) + $15,000*PVA(5%,20)*PVIF(5%,20)

Present Value Annuity Factor for 5%, 20 years= 12.46221

Present Value Interest Factor for 5%, 20 years= 0.376889

Therefore, loan amount= $10,000*12.46221 + $15,000*12.46221*0.376889

= $124,622.10 + $ 70453.05 = $ 195,075.15

Outstanding balance after 4th payment= $194,013.81

Outstanding balance after 37th payment= $ 40,848.14

Relevant portion of amortization schedule as below: