Question

Vito Scaletta just bought his dream car, a 2019 Aston Martin DB9 Carbon Edition, that cost $215,000. He paid $50,000 down and financed the balance over 84 months at 6.25% p.a. (Assume that Vito makes all required payments on time).

1. What is the monthly payment on Vito’s loan?

2. What will the balance on Vito’s loan be at the end of the fourth year (that is, immediately after Vito makes his 48th payment on the loan)?

3. What is the total amount of interest that Vito will pay over the entire term of the loan (that is, the total amount of interest that is paid on payments 1 through 84)?

Answer 1

PV of loan amount = 215,000 - 50,000 = 165,000
Number of months = 84
Rate per month = 6.25%/12

1. Monthly Payment = PV of Loan/(1-(1+r)^-n)/r = 165,000/(1-(1+6.25%/12)^-84)/(6.25%/12) = 2430.24

2. Balance at end of 48 months = PV of loan*(1+r)ⁿ - Monthly Payment*((1+r)ⁿ-1)/r = 165,000*(1+6.25%/12)⁴⁸ - 2430.24*((1+6.25%/12)⁴⁸ -1)/(6.25%/12) = 79,587.63

3. Total amount of interest in 84 months = PV*(1+r) ⁿ - PV = 165,000*(1+6.25%/12)⁸⁴ - 165,000 = 46,726.78

Please Discuss in case of Doubt

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