Question

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A five-year loan is being repaid with level monthly installments, one at the end of each...

A five-year loan is being repaid with level monthly installments, one at the end of each month beginning on 1/1/2018 and ending on 12/31/2022. A 12% nominal annual interest rate compounded monthly was used to determine the amount of each monthly installment.

In which of the following periods does the outstanding loan balance first fall below one-half of the original amount of the loan?

a) January 2018 through March 2020

b) April 2020 through June 2020

c) July 2020 through September 2020

d) October 2020 through December 2020

e) January 2021 through December 2022

Solutions

Expert Solution

Let us say the loan amount is $10,000.

Monthly loan payment is calculated using PMT function in Excel :

rate = 12% / 12   (converting annual rate into monthly rate)

nper = 5*12 (5 year loan with 12 monthly payments each year)

pv = 10000 (loan amount)

PMT is calculated to be $222.44

The loan amortization schedule is constructed as below :

Interest in any month = principal outstanding at beginning of month * 6% / 12

Principal portion of monthly payment = monthly payment minus interest portion of payment

principal outstanding at end of month = principal outstanding at beginning of month minus principal portion of monthly payment

We can see that the outstanding loan balance first falls below $5,000 (one-half of the original amount of the loan) in November 2020.

The answer is (d)

jeff jeffy answered 2 years ago
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