Question

Andy needs a loan that he will not have to pay back for 3 years. The interest rate for the

loan is 7.5% compounded quarterly. On the maturity date, wants Andy to make a single
payment of no more than $12000. What is the most Andy can borrow?

Answer 1

Answer: $9602.18

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Work Shown:

`A = P*\left(1+(r)/(n)\right)^(n*t)\\\\ 12000 = P*\left(1+(0.075)/(4)\right)^(4*3)\\\\ 12000 \approx P*1.24971638\\\\ P \approx (12000)/(1.24971638)\\\\ P \approx 9602.17869594\\\\ P \approx 9602.18\\\\`

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Explanation: I used the compound interest formula. The value of P is the amount loaned to Andy. That amount compounds interest over t = 3 years to arrive at A = 12000 dollars.

The interest rate in decimal form is r = 0.075 and n = 4 is due to quarterly compounding the interest.

The approximate result for P is the most Andy can borrow if he doesn't want A to get larger than $12,000. Smaller values of P will point to values of A such that 0 < A < 12000.