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To purchase a new truck, you borrow $42,000. The bank offers an interest rate of 7.5% compounded monthly. If you take a 5-year loan and you will be making monthly payments, what is the total amount that must be paid back?

What is the number of time periods (n) you should use in solving this problem?

What rate of interest (i), per period of time, should be used in solving this problem?

Is the present single amount of money (P) known? (Yes or No)

Which time value factor should be used to solve this problem?

What amount must be paid back each month?

What is the total amount that will be paid back over the life of the loan?

What is the total amount of interest you will pay?

Respuesta :

sqdancefan

Answer:

  • n = 60
  • i = 0.625%
  • P = 42000 (known: yes)
  • time value factor?
  • monthly payment = $841.59
  • total paid back = $50,495.40
  • total interest: $8495.40

Step-by-step explanation:

a) 5 years of monthly payments is 5×12 = 60 payments.

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b) The annual interest rate of 7.5% is divided by the number of months in a year to find the monthly interest rate: 7.5%/12 = 0.625% per month

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c) The principal amount of the loan is said to be $42,000. This is a known amount (yes).

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d) The wording "which time value factor" suggests you have choices. Since you are working with a monthly interest rate and a number of months, no additional time value factor is needed. That is, it might be 1. If you were working with an annual rate and a number of years, then the factor might be 12 (or 1/12). You will notice we multiplied years by 12, but multiplied interest rate by 1/12. We don't know what you mean by "time value factor", and we don't know what your choices are, so we cannot help with this part of the question.

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e) The monthly payment is calculated using the formula ...

  A = Pi/(1 -(1+i)^-n) = $42,000×0.00625/(1 -1.00625^-60) ≈ $841.59

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f) The total paid back is the product of the number of payments and the amount of each:*

  total repaid = 60 × $841.59 = $50,495.40

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g) The interest paid is the difference between the amount repaid and the amount borrowed:

  interest = $50,495.40 -42,000 = $8,495.40

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* In real life, the final payment will be different, so the total repaid will be slightly different than this. Since the calculated payment amount was rounded down to the nearest cent, the final payment will need to be slightly larger to pay off the loan. A spreadsheet for this loan suggests the final payment may need to be larger by $0.26, so the total repaid and the total interest amount would be larger by this value.