In: Finance
You have saved $3,000 for a down payment on a new car. The largest monthly payment you can afford is $500. The loan will have a 11% APR based on end-of-month payments.
What is the most expensive car you can afford if you finance it for 48 months? Do not round intermediate calculations. Round your answer to the nearest cent.
$ What is the most expensive car you can afford if you finance it for 60 months? Do not round intermediate calculations. Round your answer to the nearest cent. $
Principal amount of loan can be calculated using formula for EMI as:
EMI = P × r × (1 + r)n /{(1 + r)n - 1 }
P = EMI/[r × (1 + r)n /{(1 + r)n - 1 }]
Where,
P = Principal
r = rate of interest = 11 % p.a. or 0.11/12 = 0.009166667 monthly
n = No. of periods = 48
Substituting all the values in above formula, we get:
P = $ 500 / [0.009166667 x (1 + 0.009166667)48 / {(1 + 0.009166667) 48 -1}]
= $ 500 / [0.009166667 x (1.009166667)48 / {(1.009166667) 48 -1}]
= $ 500 / [0.009166667 x 1.54959805 / (1.54959805-1)]
= $ 500 / [0.009166667 x 1.54959805 / (0.54959805)]
= $ 500 / (0.01420465/ 0.54959805)
= $ 500/0.02584552
= $ 19,345.71
Total cost of car = Principal of loan + down payment = $ 19,345.71 + $ 3,000 = $ 22,345.71
If n = 60 periods,
P = $ 500 / [0.009166667 x (1 + 0.009166667)60 / {(1 + 0.009166667) 60 -1}]
= $ 500 / [0.009166667 x (1.009166667)60 / {(1.009166667) 60 -1}]
= $ 500 / [0.009166667 x 1.72891573/ (1.72891573-1)]
= $ 500 / [0.009166667 x 1.72891573/ (0.72891573)]
= $ 500 / (0.015848394/ 0.72891573)
= $ 500/0.021742423
= $ 22,996.52
Total cost of car = Principal of loan + down payment = $ 22,996.52 + $ 3,000 = $ 25,996.52
For a loan period of 48 months, $ 22,345.71 car can be affordable where as for loan period of 60 months, $ 25,996.52 car can be affordable.