Question

36. Allysha just borrowed 39,900 dollars. She plans to repay this loan by making a special payment of 5,000 dollars in 5 years and by making regular annual payments of 7,900 dollars per year until the loan is paid off. If the interest rate on the loan is 4.79 percent per year and she makes her first regular annual payment of 7,900 dollars in one year, then how many regular annual payments of 7,900 dollars must Allysha make? Round your answer to 2 decimal places (for example, 2.89, 14.70, or 6.00).

Answer 1

- Borrowed Amount Today = $39,900

Special payment will be made in 5 years = $5,000

Calculating the Present value of Special payments to be made in 5 years today:-

where, Future Value = $5,000

r = periodic Interest Rate = 4.79%

n = no of periods = 5

Present Value = $3957.04

Value of borrowed amount left after Special Payment in today terms = $39,900 - $3957.04

=$35,942.96

Now, Calculating the no of regular annual payments required to pay off the loan in today terms using Present Value of Ordinary Annuity formula:-

Where, C= Periodic Payments = $7900

r = Periodic Interest rate = 4.79%

n= no of periods

Present value = $35,942.96

(1.0479)^-n = 0.78206736912

Taking Log on both sides,

-n*Log(1.0479) = Log(0.78206736912)

-n*0.020319840 = -0.106755834

n = 5.25 payments

So, Allysha has to make 5.25 regular annual payments to pay off the Loan

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