Question

Stan borrows $20,000 at a quarterly effective interest rate of 2.1%. Stan repays the loan by making a payment of X six months from now and a payment of 2X one year from now. Three months after Stan's first payment, Stan decides to pay off his loan early. What is the amount of Stan's final payment?

Answer 1

Borrowed amount today = $20,000

Loan is to be repaid with first paymnet of X in 6 months and 2nd payment of 2X in 1 years from now.

Calculating the value of X using Present Value method:-

where, Payment1 = X

r = Quarterly effective interest rate = 2.1%

Payment2 = 2X

X = $7143.50

Amount of second payment 1 year from now = $7143.50*2

= $14287

As, Stan decides to pay 2nd payment 3 months before the prescribed date which is 9 months from now rather than 12 months from now.

We will calculate the Present value of 2nd paymnet 3 months before the prescribed date:-

PV = Payment/(1+r)^1

where, Payment = $14,287

r = Quarterly effective interest rate = 2.1%

PV = $14,287/(1+0.021)^1

= $13,993.14

So, the amount of Stan's final payment is $13,993.14

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