Question

35. Cara just borrowed 245,758 dollars. She plans to repay this loan by making a special payment of 33,047 dollars in 6 years and by making regular annual payments of 28,962 dollars per year until the loan is paid off. If the interest rate on the loan is 6.29 percent per year and she makes her first regular annual payment of 28,962 dollars immediately, then how many regular annual payments of 28,962 dollars must Cara make? Round your answer to 2 decimal places (for example, 2.89, 14.70, or 6.00).

Answer 1

- Borrowed Amount Today = $245,758

Special payment will be made in 6 years = $33,047

Calculating the Present value of Special payments to be made in 6 years today:-

where, Future Value = $33,047

r = periodic Interest Rate = 6.29%

n = no of periods = 6

Present Value = $22,918.05

Value of borrowed amount left after Special Payment in today terms = $245,758 - $22,918.05

=$222,839.95

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 = $28,962

r = Periodic Interest rate = 6.29%

n= no of periods

Present value = $222,839.95

(1.0629)^-n = 0.51603366243

Taking Log on both sides,

-n*Log(1.0629) = Log(0.51603366243)

-n*0.026492407 = -0.2873219671

n = 10.85 payments

So, Cara has to make 10.85 regular annual payments to pay off the Loan

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