A couple sold their home In addition to cash they took a mor

A couple sold their home. In addition to cash, they took a mortgage on the house. The mortgage will be paid off by monthly payments of $232.50 for 10 years. The couple decides to sell the mortgage to a lend bank. The bank will buy the mortgage, but requires a 1 % per month interest rate on their investment. How much will the bank pay for the mortgage? $21,318.14 $16,205.48 $33,215.16 $12,856.27

Solution

The formula for mortgage loan is p = L [r(1 + r)ⁿ]/[(1 + r)ⁿ - 1], where L is the loan amount, r is the monthly rate of interest in decimals, n is the period in months, for which the loan is taken and p is the monthly payment.

Here, p = $232.5, r = 1/100 = 0.01, and n = 10*12 = 120. Then, we have 232.5 = L[ 0.01( 1+ 0.01)¹²⁰]/ [( 1+ 0.01)¹²⁰ -1] or, L = 232.5 [( 1.01)¹²⁰ -1]/ [ 0.01(( 1.01)¹²⁰ ] = 232.5 ( 3.300386895 -1)/( 0.01*3.300386895) = 534.839953/0.033003868 = $ 16205.37.

The answer is $ 16205.37. The closest answer is the 2^nd option, i.e. $ 16205.48. The difference is due to a rounding off error. We may accept the 2^nd option i.e. $ 16205.48. as the answer.