A loan is being repaid with level annual payments of $1,000. Calculate the outstanding balance of the loan if there are 12 payments left. The next payment will be paid one year from now and the effective annual interest rate is 5%.

$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}

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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