Question

A debt of $9,388.81 is repaid by payments of $1,160.62 in 4 months, $1,178.29 in 13 months, and a final payment in 23 months. If interest was 4% compounded semi-annually, what was the amount of the final payment?

Answer 1

after 4 months $8352.96

AFTER 13 MONTH $7426.507

AFTER 23 MONTH A = 7675.69

Explanation:

Given data:

P = $9388.81

Compound interest cab be determined as

A = P( 1+ r/n)^(nt)

after 4 months

`A = 9388.81 ( 1+ (4)/(100))^{2* (4)/(12)}`

A = 9513.58

But he has to pay $1160.62 after 4 month so remaining amount is

P = 9513.58 - 1160.62 = $8352.96

AFTER 13 MONTH, so total time is 9 month

`A = 8352.96 ( 1+ (4)/(100))^{2* (9)/(12)}`

A = 8604.79

But he has to pay $1178.29 after 13 month so remaining amount is

P = 8604.79 - 1178.28 = $7426.507

AFTER 23 MONTH so total time is 10 month

`A = 7426.50 ( 1+ (4)/(100))^{2* (10)/(12)}`

A = 7675.69