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A loan is being repaid with 20 payments of $ 1,000 at the end of each...

A loan is being repaid with 20 payments of $ 1,000 at the end of each quarter. Given that the nominal rate of interest is 8% per year compounded quarterly, find the outstanding balance of the loan immediately after 10 payments have been made (a) by the prospective method, (b) by the retrospective method.

Solutions

Expert Solution

First we find the loan amount at the start

Rate  = 2% (8%/4 = 2% rate per quarterly period)

PV = 1000*[(1-(1+0.02)^(-20))/0.02]

PV = $16351.43

Hence, the loan initially = $16351.43

(a) by the prospective method

Loan balance outstanding is the PV of all the future payments

Loan balance outstanding PV

PV = 1000*[(1-(1+0.02)^(-10))/0.02]

we get PV = 8982.59

Hence, $8982.59 is the outstanding balance using prospective method

(b) by the retrospective method.

Loan balance outstanding is the FV of loan after 10 intallments - FV of all the 10 installments

FV of all the 10 installments FV

FV = 1000*[((1+0.02)^10)-1)/0.02]

FV = 10949.72

Hence, accumulated installments after 10 installments = $10949.72

FV of loan after 10 intallments = 16351.43*(1.02^10) = $19932.30

Loan balance outstanding = $(19932.30-10949.72) = $8982.59

Hence, $8982.59 is the outstanding balance using retrospective method

jeff jeffy answered 2 years ago
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