Question

You are thinking about a piece of art that costs $50,000. The art dealer proposes the following deal: He will lend you the money, and you will repay the loan by making the same payment every three months for the next 20 years (i.e. 80 total payments). If the interest rate is 6% APR with monthly compounding, how much will you have to pay every three months? $1,080.03 $1,027.99 No answer is within $10 of the correct answer $1,101.23 $1,133.42

Answer 1

You buy a piece of art by borrowing at = $50,000

You will have to Make payments every 3 months, while interest is 6% compounded monthly. We will convert interest rate into 3-month interest rate from monthly compounding.

$3-monthly Interest rate = (1+\frac{r}{m})^3-1$

where, r = Interest rate = 6%

m = no of times compounding = 12

$3-monthly Interest rate = (1+\frac{0.06}{12})^3-1$

= 1.5075125%

Calculating the Quarterly payments of loan:-

$Quarterly Payment = P*r*\frac{(1+r)^{n}}{(1+r)^{n}-1}$

wheer, P = Loan Amount = $50,000

r = Periodic interest Rate = 1.5075125%

n = no of periods = 80

(1 + 0.015075125) SO Quarterly Payment = 50,000 * 0.015075125 * (1 +0.015075125) 80 – 1

$Quarterly Payment = 50,000*0.015075125*\frac{3.31020447581}{3.31020447581-1}$

Quarterly Payment = $1080.03

So, Payment every 3-months is $1080.03

Option 1

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