Erin borrows $40,000 at 7% interest (per year) for purchasing assets which appre

Question

Erin borrows $40,000 at 7% interest (per year) for purchasing assets which appreciate in value at 4% per year. Suppose Erin holds her assets, repaying the loan from her monthly income by constant monthly amounts. The loan is fully repaid at the end of five years.Assume that the interest on the loan as well as the asset appreciation are compounded monthly. At the end of five years,

i. What were Erin's monthly payments?

ii: How much did Erin pay in interest?

iii: By what amount did Erin's assets increase in value?

Explanation / Answer

i).

loan amount, PV = $40,000

interest rate, r= 7%

monthly interest rqate = 7/12 = .5833%

no of months = 12*5 = 60 month

let monthlly payment = PMT

PV = PMT*PVIFA(.5833,60)

PMT = 40,000/50.5020 = $792.047

monthly payment will be $792.047

ii).

amount erin paid as interest = total amount paid in 5 years-loan amount

= 792.047*60-40,000 = $7522.82

iii).

amount at which asset appreciated = (40,000*(1.04)^5)-40000 = $8666.11

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