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Brittany received a loan of $30,000 at 6.25% compounded monthly. She had to make payments at the end of every month for a period of 5 years to settle the loan. a. Calculate the size of payments

User JEV
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Final answer:

To calculate Brittany's monthly payment, convert the annual interest rate to a monthly rate, determine the total number of payments, and use the amortizing loan payment formula. With the given values, a calculator will provide the exact payment amount.

Step-by-step explanation:

To calculate the size of the monthly payments for Brittany's loan of $30,000 at an interest rate of 6.25% compounded monthly over a period of 5 years, we use the formula for the monthly payment (M) of an amortizing loan:

M = P [ i(1 + i)^n ] / [ (1 + i)^n − 1 ]

Where:

  • P = principal amount ($30,000)
  • i = monthly interest rate (annual rate / 12)
  • n = total number of payments (years × 12)

First, calculate the monthly interest rate:

i = 6.25% per year / 12 months = 0.0625 / 12 = 0.0052083

Next, calculate the total number of payments:

n = 5 years × 12 months/year = 60 payments

Now, substitute the values into the formula to find the monthly payment:

M = 30,000 [ 0.0052083(1 + 0.0052083)^60 ] / [ (1 + 0.0052083)^60 − 1 ]

A calculator is needed to compute the exact monthly payment. The resulting figure will be the amount Brittany needs to pay each month to settle the loan at the end of 5 years.

User Mjrezaee
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