You take out a 40 year loan with effective annual interest i = .05 and yearly...

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.

Solutions

Expert Solution

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:

jeff jeffy answered 1 year ago

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