Question

In: Finance

You have saved $3,000 for a down payment on a new car. The largest monthly payment...

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. $

Solutions

Expert Solution

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.


Related Solutions

You have saved $4,000 for a down payment on a new car. The largest monthly payment...
You have saved $4,000 for a down payment on a new car. The largest monthly payment you can afford is $450. The loan will have a 9% 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...
You have saved $5,000 for a down payment on a new car. The largest monthly payment...
You have saved $5,000 for a down payment on a new car. The largest monthly payment you can afford is $450. The loan will have a 6% APR based on end-of-month payments. What is the most expensive car you can afford if you finance it for 48 months? For 60 months? Do not round intermediate calculations. Round your answers to the nearest cent. Financed for 48 months: $   Financed for 60 months: $   Find the present values of the following...
a. You have saved $5,000 for a down payment on a new car. The largest monthly...
a. You have saved $5,000 for a down payment on a new car. The largest monthly payment you can afford is $450. The loan will have a 12% APR based on end-of-month payments. What is the most expensive car you can afford if you finance it for 48 months? For 60 months? Do not round intermediate calculations. Round your answers to the nearest cent. Financed for 48 months: $   Financed for 60 months: $   Bank A pays 6% interest compounded...
saved $3000 for a down payment on a car. the largest monthly payment you can afford...
saved $3000 for a down payment on a car. the largest monthly payment you can afford is $400. The loan will be at 8%APR based on end of month payments. a) What is the most expensive car you can afford if you finance for 48 months? b) What is the most expensive car financing 60 months?
You have saved $10,000 for a down payment on the purchase of a new car, however,...
You have saved $10,000 for a down payment on the purchase of a new car, however, since you plan to buy the car one year from today, you need to decide how to invest the money for one year. You are limited to one of two choices: 1. A Bond Fund with an expected return of 3%/year 2. A Stock Fund with an expected return of 7%/year. Which fund is best? Explain why!
PV AND LOAN ELIGIBILITY You have saved $5,000 for a down payment on a new car....
PV AND LOAN ELIGIBILITY You have saved $5,000 for a down payment on a new car. The largest monthly payment you can afford is $300. The loan will have a 12% 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...
You have saved $50,000 to use as a down payment for some property and to build...
You have saved $50,000 to use as a down payment for some property and to build a home. The home is in a prime building location that has trees and a stream running through the property. The clearing of the land and the building of the house will cost a total $650,000. a.     How much money will you need to borrow through a loan for your home? b.     The bank offers to finance your purchase with a 25-year amortized loan with a...
In order to buy a new car, you finance $23,000 with no down payment for a...
In order to buy a new car, you finance $23,000 with no down payment for a term of five years at an APR of 6%. After you have the car for one year, you are in an accident. No one is injured, but the car is totaled. The insurance company says that before the accident, the value of the car had decreased by 25% over the time you owned it, and the company pays you that depreciated amount after subtracting...
Ross purchased a new commercial vehicle today for $25,000 with a down payment of $3,000. The...
Ross purchased a new commercial vehicle today for $25,000 with a down payment of $3,000. The amount was financed using a five-year loan with a 4 percent interest rate (compounded monthly). How much will Ross owe on his vehicle loan after making payments for three years?
You will have to search for your dream house, calculate the down payment, and the monthly...
You will have to search for your dream house, calculate the down payment, and the monthly payments for a 30 and 15 years fixed loan. You will use the loan payment formula to determine your monthly payments for a 30-year fixed loan with an APR of 3.75% and for a 15-years fix loan with an APR of 2.97% with a down payment of 5%. You will make a decision on which loan you would take and provide reasons for your...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT