Question

Please use engineering economy relations. no excel.

Problem 3: A family decided to buy a super ski and water sports boat. They took out an $80,000,5-year, 6% per year, compounded monthly loan with monthly payments from their bank. After making only two payments, a banker friend offered to make them a better deal: a 5-year, 4.2% per year, compounded monthly loan. The principal on the new loan will be the remaining principal from the current loan. Answer the following questions: (a) What is the current monthly payment on the $80,000 loan? (b) What is the principal due on the current loan after 2 months? (c) How much interest have they already paid in the first two payments? (d) What is the amount of the new monthly payment starting with month 3, if the new loan offer is accepted?

Answer 1

Solution

Given:

Details of current loan:

Principal = $80,000 ; Time = 5 year ; Interest = 6% p.a,compounded monthly => monthly rate = 0.5%

=> Effective interest rate / effective annual interest rate = [ { [( 0.5 / 100) + 1] ^ (12)} - 1] * (100)

=> 6.16% p.a

It is calculated as : monthly installment = P * r * [ (1+r) ^ n) /(((1+r) ^ n) - 1) ]

where r = annual interest rate / 12 / 100

= 80,000 * (0.00513) * (1.00513 ^ 60) / ((1.00513 ^ 60) - 1)

= 80,000 * (0.00513) * (1.359 / 0.359)

= $1553.575 ~ $1553.57 per month

(b) principal due after 2 months :

principal per month = 80,000 / 60 i.e., $1333.33

So, principal due after 2 months is : 80,000 - ( $1333.33 * 2) => $ 77,333.34

(c) Interest already paid in 1 st 2 installements = (1553.57 - 1333.33) * 2 => $440.48

(d) From month 3 onwards the new monthly installment for new loan repayment is :

Principal = $77,333.34 ; Time = 5 year ; Interest = 4.2% p.a,compounded monthly => monthly rate = 0.35%

=> Effective interest rate / effective annual interest rate = [ { [( 0.35 / 100) + 1] ^ (12)} - 1] * (100)

=> 4.28% p.a

It is calculated as : monthly installment = P * r * [ (1+r) ^ n) /(((1+r) ^ n) - 1) ]

where r = annual interest rate / 12 / 100

= 77333.34 * (0.00356) * (1.00356 ^ 58) / ((1.00356 ^ 58) - 1)

= 77333.34 * (0.00356) * (1.228 / 0.228)

= $1482.79  per month