Question

Sally wants to buy a car but is unsure how much of . she can afford. The maximum monthly payment she can afford is $780.. Her bank’s interest rate is 14%. annually if she pays off the loan over 5 years. What is the maximum amount she can afford to borrow?   

1. Impossible to calculate given the available data
2. She can afford $53, 352.05
3. She can afford $46,800.03

D-She can afford $33,522,07   

Someone said all options are wrong, can you calculate and show work?

Answer 1

Loan repayment of $ 780 per month represents an ordinary annuity structure.

Ordinary annuity is defined as series of consecutive payment for a fixed period.

Further, maximum amount she can borrow is equal to present value of monthly repayment amount, which she can.

Present value of annuity = PMT /R% ( 1- (1+R%)^-N)

Where, PMT is regular payment
R% is rate of return
and N is time period.
Here,
Monthly Repayment (PMT) = $ 780
Rate of return (R%) = 14%/12 = 1.1667%
Time Period (N) = 5 Years * 12 = 60 months
Present value of repayment = $ 780/ 1.1667% * ( 1- ( 1+1.1667%)^-60)
Present value of repayment = $ 66,857.1429 * ( 1- ( 1.011667)^-60)
Present value of repayment = $ 66,857.1429 * ( 1- 0.498601)
Present value of repayment = $ 66,857.1429 * 0.50139
Present value of Investment = $ 33,522.0728
Answer : $ 33,522.07
As, present value of her repayent is $ 33,522.07 . She can afford to borrow it.