Ian loaned his friend $20,000 to start a new business. He considers this loan to

Question

Ian loaned his friend $20,000 to start a new business. He considers this loan to be an investment, and therefore requires his friend to pay him an interest rate of 8% on the loan. He also expects his friend to pay back the loan over the next our years by making annua payments atthe end of each year an texted and asked that you help him calculate the annual payments that he should expect to receive so that he can recover his initial investment and earn the agreed-upon 8% on his investment. Calculate the annual payment and complete the following capital recovery schedule: Beginning Amount Interest Paid Principal Paid Year Payment Ending Balance 1 $20,000.00 4 $0.01

Explanation / Answer

Let X be the Annual Repayment amount.
This means that present value of X discounted @ 8% should give the loan value i.e $20000.
i.e
$20000 = X/1.08 + X/1.08^2 + X/1.08^3 + X/1.08^4.

or $20000 = X(1/1.08 + 1/1.08^2 + 1/1.08^3 + 1/1.08^4 )

or $20000 = 3.3121 X

or X = $6038 (Ans)

Ans : The annual repayment value is $6038.
____________________________________________________________

The capital recovery schedule is :

Calculation Logic (Beginning Amount * 8%) Payment - Interest Paid Beginning Amount - Principal Paid Year Beginning Amount Payment Interest Paid. Principal Paid Ending Balance 1 20000 6038 1600 4438 15562 2 15562 6038 1244.96 4793.04 10768.96 3 10768.96 6038 861.5168 5176.4832 5592.4768 4 5592.4768 6038 447.398144 5590.601856 0

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