Question

A loan of 20,000 is being repaid by 20 annual payments at the end of year, each includes equal repayment of the principal along with the interest at 5% effective on the unpaid loan balance. After receiving each payment, the lender immediately deposits the payment into an account bearing interest at an annual rate of 3%. Find the accumulated value of the account right after the last deposit. The accumulated value is (in two decimals).

Answer 1

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Calculation of annual installment of loan

Loan Amount = PV = 20,000

n = 20

r = 5%

Annual Loan Amount = [r*PV] / [1 - (1+r)^-n]

= [20,000 * 5%] / [1 - (1+5%)^-20]

= 1,000 / 0.62311051712

= 1604.85174383

Annual loan amount is 1,604.85

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Annual deposit amount = P = 1,604.85

n = 20 years

r = 3%

Future value of annuity = P [(1+r)^n - 1] / r

= 1,604.85 [(1+3%)^20 - 1] / 3%

= 1,604.85 * 0.80611123466 / 0.03

= 43122.9204986

Therefore, Accumulated value is 43,122.92