Question

A successful businessman is selling one of his fast food franchises to a close friend. He is selling the business today for $2,156,200.00. However, his friend is short on capital and would like to delay payment on the business. After negotiation, they agree to delay 5.00 years before the first payment. At that point, the friend will make quarterly payments for 11.00 years. The deal calls for a 9.80% APR “loan” rate with quarterly compounding. What quarterly payment will the friend make on the loan?

Answer #1

The friend delays the repayments by 5 years post which he/she starts making quarterly repayments. This implies that the first repayment comes in at 5 (and not 5.25), second at 5.25, third at 5.5 and so on for a total tenure of 11 years or (11 x 4) = 44 quarters.

APR = 9.8 % compounded quarterly

Quarterly Interest Rate = (9.8/4) = 2.45 % and Borrowing = $ 2156200

Let the equal quarterly repayments be $ K

Therefore, 2156200 = K x (1/0.0245) x [1-{1/(1.0245)^(44)}] x (1.0245) x [1/(1.0245)^(20)]

K = $ 127690.7

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