Question

Julie and Bell apply for a $60,000 loan. Contractual rate is 8 % with 6 annual payments. (40 points) Show all your work using the appropriate formulas

a. What are the annual payments (if you use constant (equal) payments method)?

b. What is the cost of the loan (total interest) if you use the method on part a?

c. What are the annual payments if you use constant payment on capital method) Make a table to show initial balance, interest paid, capital paid, and remaining balance.

d. What is the cost of the loan (total interest) if you use the method on part c) Now assume that the bank uses add-on method for the same loan ($60.000). The contractual rate is 8% with 6 annual equal payments.

e. What are the annual payments?

f. What is the effective interest rate of the loan? Now assume that the bank uses discount method for the same loan ($60.000). The contractual rate is 8% with 6 annual equal payments.

g. What are the annual payments?

h. What is the effective interest rate of the loan?

Answer 1

a). Equal payment: PV = 60,000; rate = 8%; N = 6, solve for PMT.

Equal annual payment = 12,978.92

b). Cost of the loan = total amount paid - loan amount = (equal annual payment*N) - 60,000 = (12,978.92*6) - 60,000 = 17,873.54

c). Constant payment on capital method table:

d). Cost of the loan = total interest paid = 4,800 + 4,000 + 3,200 + 2,400 + 1,600 + 800 = 16,800

e). Total interest payable = loan amount*annual rate* number of payments = 60,000*8%*6 = 28,800

Total amount payable = total interest + loan amount = 28,800 + 60,000 = 88,800

Annual payment = total amount/number of payments = 88,800/6 = 14,800

f). Effective interest rate on the add-on can be calculated using the annuity formula: PV = 60,000; PMT = -14,800; N = 6, solve for RATE.

Effective interest rate = 12.50%