Question

A young executive is going to purchase a vacation property for investment purposes. She needs to borrow $111,000.00 for 27 years at 5.1% compounded monthly, and will make monthly payments of $631.59. (Round all answers to 2 decimal places.)

What is the unpaid balance after 10 months? ____

During this time period, how much interest did she pay? _____

Answer 1

The formula used to calculate the remaining loan balance (B) of a fixed payment loan of $ L, over a term of n months, after p months, is B=L[(1+r )ⁿ- (1+ r)^p]/[(1+ r)ⁿ- 1] where r is the monthly rate of interest.

Here, L = 111000, n =27 *12=324 ,p=10 and r=5.1 %/12=5.1/1200 = 0.00425. Hence B = 111000[(1.00425)³²⁴ -(1.00425)¹⁰ ]/[ (1.00425³²⁴ -1] = 111000( 3.951448179-1.043322093)/ (3.951448179-1) = 111000*2.908126086/2.951448179 = 109370.71 ( on rounding off to the nearest cent).

Thus. the unpaid balance after 10 months is $ 109370.71.

The total amount paid by the executive during 10 months is 10*$ 631.59 = $ 6315.90. The reduction in the amount of the loan in 10 months is $ 111000-$ 109370.71 = $ 220.37 . Hence, the interest paid by the executive during 10 months is $ 6315.90- $ 220.37 = $ 6095.53.