Question

You borrowed $20,000 from a bank at an
interest rate of 12%, compounded monthly.
This loan will be repaid in 60 equal monthly
installments over 5 years. Immediately after
your 30th payment if you want to pay the
remainder of the loan in a single payment, the
amount is close to:

Answer 1

Monthly rate = 12% / 12 = 1%

Present value = Annuity * [1 - 1 / (1 +r)^n] / r

20,000 = Annuity * [1 - 1 / (1 + 0.01)^60] / 0.01

20,000 = Annuity * [1 - 0.55045] / 0.01

20,000 = Annuity * 44.955038

Annuity = 444.89

Number of periods remaining = 60 - 30 = 30

Present value = Annuity * [1 - 1 / (1 + r)^n] / r

Present value = 444.89 * [1 - 1 / (1 + 0.01)^30] / 0.01

Present value = 444.89 * [1 - 0.741923] / 0.01

Present value = 444.89 * 25.807708

Present value = $11,481.59

Single payment should be $11,481.59