You want to borrow $75,000 from your local bank to buy a new sailboat. You can a

Question

You want to borrow $75,000 from your local bank to buy a new sailboat. You can afford to make monthly payments of $1,400, but no more.

Assuming monthly compounding, what is the highest rate you can afford on a 66-month APR loan?(Round your answer as directed, but do not use rounded numbers in intermediate calculations.Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)

Assuming monthly compounding, what is the highest rate you can afford on a 66-month APR loan?(Round your answer as directed, but do not use rounded numbers in intermediate calculations.Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)

Explanation / Answer

Answer: APR = 7.81%

Calculations are given below:

The $ 75,000 that is to be borrowed can be considered as the Present Value of the monthly payments (annuity) of $1,400.

Hence, 75,000 = 1400 * PVIFA(i,66)

75000/1400 = 53.5714

Looking at the PVIFA table

the value for 0.50% is 56.0970 and

the value for 0.75% is 51.9070

so % for 53.5714 = 0.75 - 0.25(1.6644/4.19) = 0.75 - 0.09931 = 0.6507%

APR = 0.6507 * 12 = 7.81 %

(Effective Annual Rate = (1+0.006507)12 - 1 = 1.08094 - 1 = 0.08094 = 8.09%)

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