Question

Wendy takes out a loan for 60,000 with 35 quarterly payments. For the first 15 payments, Wendy will pay only the interest due at the end of each quarter. For the remaining payments, Wendy will pay K at the end of each quarter. Suppose that the annual effective interest rate on the loan is 5.5%. Calculate (a) The total of all Wendy’s payments for this loan. (b) The total interest paid by Wendy on the loan.

Answer 1

Here, Wendy only pays interest on the first 15 quarters. So let us first find the Interest on one of these quarters.

Interest per quarter = $60,000 * (5.5% / 4) = $825  ................................... (1)

Now to find 'k', we can use the present value of annuity formula:

Where,
PVA = Present Value of Annuity / Amount of loan
A = Payment OR k
i = rate of interest
a = number of payments per year
na = total number of payments

So let us put the value in the equation.

or k = 3451.832201

So the next 20 quarterly payments will be $3,451.83 each. .......................(2)

From the above solution we can answer the questions.

a) Total of all Wendy's payments

From (1) and (2), we can answer this,

Therefore, total of all Wendy's payments for this loan = $81,411.64 ..............................(3)

b) The total interest paid by Wendy on the loan.

From (3), we know the total payment done by Wendy is $81,411.64

We also know the amount of loan was $60,000

Therefore, total interest paid by Wendy = $81,411.61 - $60,000 = $21,411.64