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?

Home Equity Loan is truly cheaper

Explanation:

Data provided in the question:

APR of the loan taken = 6.9% = 0.069

Interest rate on Loan for boat per annum

=

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

t = time = 1 year = 12 months

thus,

Annual Interest rate on Loan for boat =

= 7.12%

APR on home equity loan = 7.9% = 0.079

Annual Interest rate on Home Equity Loan =

= 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

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.