Question

1. A loan is made in the amount of $13,675. The interest rate is 6% and equal payments are to be made semi-annually over 4 years. SHOW ALL WORK!!
2. 1. What is the amount of each payment?
3. 2. What is the total installment cost for the loan?   
4. 3. What is the finance charge for the loan?                                                                               

Answer 1

Installments = Loan amount/PVIFA(r%,n)

here r = rate of interest = 6% / 2 = 3%

n = no of interest payments = 4 x 2 = 8

PVIFA(r%,n) = [1-(1/(1+r)^n / r ]
PVIFA(3%,8) = [1-(1/(1+3%)^8/ 3%]
=[1-(1/(1+0.03)^8 / 0.03]
=[1-(1/(1.03)^8 / 0.03]
=[1-0.7894 / 0.03]
=0.21059/0.03
=7.01969

Thus Installments = 13675/7.01969

=1948.09 $

Thus

amount of each payment = 1948.09$

Total installment cost of loan = 1948.09 x 8 = 15584.73 $

Finance charge of loan = Total installment cost - Loan amount

= 15584.73 - 13675

=1909.73 $