Question

You want to borrow $90,000 from your local bank to buy a new sailboat. You can afford to make monthly payments of $1,700, but no more. Assuming monthly compounding, what is the highest rate you can afford on a 60-month APR loan? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) interest rate %

Answer 1

Amount to be borrowed: $ 90,000

Maximum payment per month = $ 1,700

Tenor = 5 year = 60 months = No. of periods

Highest Serviceable Interest Rate: To find this rate, the discounted cash flows ($1,700) for the next 60 months at 'X%' rate should be equal to $90,000.

90,000 = 1700 / (1+x%)^^1/12  + 1700 / (1+x%)^^2/12 + ...... + 1700 / (1+x%)^^25/12 + ...... + 1700 / (1+x%)^^46/12 + 1700 / (1+x%)^^60/12

However, it is not possible to solve this formula. Hence, we must use the excel formula of rate.

=Rate ( No. of periods , Payment per month , Present Value , Future Value , Payment at beginning/end) x 12

The value from formula is multiplied by 12 to get the annualized rate since we are considering monthly payment

=Rate(60,1700,-90000,0,0) x 12

=0.42% x 12

=5.0385% = 5.04%

Hence, the maximum rate which can be serviced is 5.04%