A student takes out a $10,000, 10-year loan with two possible repayment plans, (i) immediate repayment or (ii) a grace period during the college years. The student takes 5 years to graduate. The interest rate is 8%, compounded annually and the loan is paid off as a yearly lump sum. Since the bank is a for-profit business (beholden to its shareholders and required to maximize profit), the bank intends to receive the same return on this loan either way. How much are the annual payments under option (i) and option (ii)

Answer and Explanation:

The calculation is given below:

(i) Immediate Repayment:

Let us assume the annual repayments be $ P

So

$10,000 = P × (1 ÷ 0.08) × [1 - {1 ÷ (1.08)^(10)}]

$10,000 = P × 6.71008

P = $10,000 ÷ 6.71008

= $1490.3

(ii) Grace Period of 5 years:

Let us assume the annual repayments be $N

Now  

Accumulated Loan Value after 5 years is

= $10,000 × (1.08)^(5)

= $14,693.3

So, $14,693.3 = N × (1 ÷ 0.08) × [1-{1 ÷ (1.08)^(10)}]

$14,693.3 = N × 6.71008

N = 14693.3 ÷ 6.71008

= $2189.74

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