Question

a) Determine Ken's present value at time 0 of payments of $480 at the end of each quarter for 8 years. The annual effective rate of interest is 6%. Show manual calculations.

b) Edward takes out a loan today and repays the loan with 8 level annual payments, with the first payment 1 year from today. The principal portion of the fifth payment is 699.68. The payments are calculated based on an annual effective interest rate of 4.75%. Calculate the total amount of interest paid on Edward's loan. Show manual calculations.

Answer 1

a. The quarterly rate will be 6/4 = 1.5%. The Present Value will be:

PV = 480/1.015 + 480/1.015^2 + ....... + 480/1.015^32 = 12128.23

B. Since the fifth payment's principal payment is 699.68, we calculate the principal remaining till the 4th payment.

If the equal payments are A,

A/1.0475 + A/1.0475^2 + A/1.0475^3 + A/1.0475^4 +  A/1.0475^5 + A/1.0475^6 + A/1.0475^7 + A/1.0475^8 = P (principal)

A - [P - (A/1.0475 + A/1.0475^2 + A/1.0475^3 + A/1.0475^4)] x 0.0475 = 699.68 (Here, we have calculated the principal paid in the 5th installment)

A - ( A/1.0475^5 + A/1.0475^6 + A/1.0475^7 + A/1.0475^8 ) x 0.0475 = 699.68

A - 0.1407A = 699.68

A = $814.2573

Total interest paid = 8 x A - P = 8 x A - (A/1.0475 + A/1.0475^2 + A/1.0475^3 + A/1.0475^4 +  A/1.0475^5 + A/1.0475^6 + A/1.0475^7 + A/1.0475^8) = 8A - 6.53A = 1.471A = 1.471 x 814.2573 = $1197.743