Question

Your uncle Fred just purchased a new boat. He brags to you about the low 6.9 % interest rate​ (APR, monthly​ compounding) he obtained from the dealer. The rate is even lower than the rate he could have obtained on his home equity loan ​(7.9 % ​APR, monthly​ compounding). But if his tax rate is 27 % and the interest on the home equity loan is tax​ deductible, which loan is truly​ cheaper?

Answer 1

Home Equity Loan is truly cheaper

Step-by-step explanation:

Data provided in the question:

APR of the loan taken = 6.9% = 0.069

Interest rate on Loan for boat per annum

=
`(1 + (r)/(n))^(t)-1`

n = number of periods = 12 [when compounded monthly]

t = time = 1 year = 12 months

thus,

Annual Interest rate on Loan for boat =
`(1 + (0.069)/(12))^(12)-1`

= 7.12%

APR on home equity loan = 7.9% = 0.079

Annual Interest rate on Home Equity Loan =
`(1 + (0.079)/(12))^(12)-1`

= 8.51%

Tax saving on interest paid @ 25% = 0.25 × Annual Interest rate

= 0.25 × 8.51

= 2.1275% ≈ 2.13%

Therefore,

Total Interest cost on home equity loan

= Annual Interest rate - Tax saving on interest paid

= 8.51% - 2.13%

= 6.38%

Hence,

Home Equity Loan is truly cheaper