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erik [133]
3 years ago
6

A loan is being repaid with level annual payments of $1,000. Calculate the outstanding balance of the loan if there are 12 payme

nts left. The next payment will be paid one year from now and the effective annual interest rate is 5%.
Business
1 answer:
aleksley [76]3 years ago
3 0

Answer:

$8,306.75

Explanation:

we are given the payment, the interest rate and the number of periods remaining, and we must first determine the principal amount:

P = (A x {([1+i]ⁿ)-1}) / {i[1+i]ⁿ}

  • A = $1,000
  • i = 5%
  • n = 12

P = ($1,000 x {([1+0.05]¹²)-1}) / {0.05[1+0.05]¹²}

P = ($1,000 x 0.79586) / 0.08979

P = $795.86 / 0.08979 = $8,863.57

Now we must determine the interest accrued in 1 year:

interest accrued in 1 year = principal x interest rate = $8,863.57 x 5% = $443.18

principal balance after the payment in 1 year = principal - (payment - interest expense) = $8,863.57 - ($1,000 - $443.18) = $8,306.75

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