Question

# A young executive is going to purchase a vacation property for investment purposes. She needs to...

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? _____

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.

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