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Suppose that you decide to borrow $15,000 for a new car. You can select one of the following loans, each requiring regular monthly payments. Installment Loan A: three-year loan at 5.5% Instaliment Loan B: five-year loan at 5.8%

Use PMT = (P(r/n)) /(1-(1+r/n)⁻ⁿᵗ)
a. Find the monthly payments and the total interest for Loan A.

User Douggard
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2 Answers

4 votes

Final answer:

To find the monthly payments for Installment Loan A, we use the given formula, plugging in the principal amount of $15,000, the annual interest rate of 5.5%, and the loan term of 3 years with monthly compounding. Calculate the monthly payment and total interest to get the precise figures.

Step-by-step explanation:

To calculate the monthly payments for Installment Loan A, which is a three-year loan at 5.5%, we'll use the provided loan payment formula. First, we must convert all values to their respective monthly amounts and plug them into the formula:




PMT = \(\frac{P(r/n)}{1-(1+r/n)^{-nt}}\)\



Where:



  • P is the principal amount of the loan, which is $15,000
  • r is the annual interest rate, which is 0.055 for 5.5%
  • n is the number of times that interest is compounded per year, which is 12 in this case
  • t is the number of years for the loan, which is 3 years



Plugging these values into the formula, we get:




PMT = \(\frac{$15,000 * (0.055/12)}{1 - (1 + 0.055/12)^{-3 * 12}}\)



Then, calculate the monthly payment and total interest:



Monthly Payment: PMT

Total Interest: 36 * PMT - $15,000



Calculate this using a calculator to get the actual figures for PMT and the total interest paid over the life of the loan. The student can now clearly see how to compute the monthly payments and total interest for Installment Loan A.

User Andrey Korneyev
by
8.0k points
2 votes

Final answer:

To find the monthly payments for Installment Loan A, we use the given formula, plugging in the principal amount of $15,000, the annual interest rate of 5.5%, and the loan term of 3 years with monthly compounding. Calculate the monthly payment and total interest to get the precise figures.

Step-by-step explanation:

To calculate the monthly payments for Installment Loan A, which is a three-year loan at 5.5%, we'll use the provided loan payment formula. First, we must convert all values to their respective monthly amounts and plug them into the formula:




PMT = \(\frac{P(r/n)}{1-(1+r/n)^{-nt}}\)\



Where:



  • P is the principal amount of the loan, which is $15,000
  • r is the annual interest rate, which is 0.055 for 5.5%
  • n is the number of times that interest is compounded per year, which is 12 in this case
  • t is the number of years for the loan, which is 3 years



Plugging these values into the formula, we get:




PMT = \(\frac{$15,000 * (0.055/12)}{1 - (1 + 0.055/12)^{-3 * 12}}\)



Then, calculate the monthly payment and total interest:



Monthly Payment: PMT

Total Interest: 36 * PMT - $15,000



Calculate this using a calculator to get the actual figures for PMT and the total interest paid over the life of the loan. The student can now clearly see how to compute the monthly payments and total interest for Installment Loan A.

User Chickenchilli
by
7.8k points