Question

A bank customer borrows X at an annual effective rate of 12.5% and makes level payments at the end of each year for n years.(which fully repays the loan).
i. The interest portion of the final payment is 142.78.
ii. The total principal repaid as of time (n − 1) is 6009.12.
iii. The principal repaid in the first payment is Y .

Calculate Y

Answer 1

Answer:

Y = $391.10

Explanation:

We have 0.125B(n-1) = i

B(n-1) = In = 142.78

So that B(n-1) = 142.78/0.125 = 1142.24

Furthermore, B(n-1) = Px = Pv = P/(1+0.125) = 1142.24

P/1.125 = 1142.24

P = 1142.24*1.125

P = 1285.02.

The total amount of the loan = Principal repaid as of time (n-1) + Principal repaid in last payment

= 6009.12 + 1142.24

= 7151.36

So, the total amount of the loan is 7151.36.

The principal repaid in the first payment Y = 1285.02 - 0.125*7151.36

Y = 1285.02 - 893.92

Y = $391.10