Question

A successful businessman is selling one of his fast food franchises to a close friend. He is selling the business today for $2,852,400.00. However, his friend is short on capital and would like to delay payment on the business. After negotiation, they agree to delay 4.00 years before the first payment. At that point, the friend will make quarterly payments for 19.00 years. The deal calls for a 5.68% APR "loan" rate with quarterly compounding. What quarterly payment will the friend make on the loan?

Answer 1

Answer:

Ans. The quarterly payment that the friend will make on the loan is $77,188.44

Explanation:

Hi, well, if they agreed to wait for 4 years to start to pay, it doesn´t mean that interest are not accumulating, therefore, $2,852,400 will accumulate interests for 4 years and the final balance will be the amount to use in order to find the equal quartely payments, but first, let´s convert this compunded interest rate into an effective rate, that is:

$Effective QuartelyRate=\frac{CompoundedRate}{4} =\frac{0.0568}{4}=0.0142$

Ok, now let´s get back to the waiting period, that is 4 years, it means 16 quarters, so the present value in year 4 is:

$PresentValue(4)=2,852,400(1+0.0142)^{16} =3,574,276.35$

Now, he has to pay for 19 years, that is 76 quarters, and the formula to use is as follows.

$PresentValue(4)=\frac{A((1+r)^{n}-1) }{r(1+r)^{n} }$

And we solve for "A"

$3,574,276.35=\frac{A((1+0.0142)^{76}-1) }{0.0142(1+0.0142)^{76} }$

$3,574,276.35=\frac{1.920075444}{0.041465071} A$

$3,574,276.35 =A(46.30585173)$

$A= 77,188.44$

Best of luck.