Question

An estate worth $3,500,000 and earning 24% per annum compounded monthly makes equal payments of $75,000 at the end of each month to Betty and Bob.
a. Algebraically determine how many payments they will receive.
b. Algebraically determine the amount of the last payment that will settle the estate.
(I need a step-by-step explanation of the formulas used. Thanks)

Answer 1

a.

1-(1+0.02) 3,500,000 = 75,000x| 0.02 46.667 =- 1-(1+0.02) 0.02 0.93333 =1-(1.02)" 1.02-" =1-0.9333 1.02-" =0.066667 -nlog 1.02 = log 0.066667 log 0.066667 -n=- log1.02 -n=-136.75

There are total 137 payments.

b.

(1-(1+0.02)=136). X 3,500,000 = 75,000x1 = soos mooo 0.02 * (1.02) 57 - - 3,500,000 = 75,00046.6166522+- (1.02) 137 3,500,000 = 3,496, 248.915+- (1.02)'37 3,500,000 - 3,496, 248.915=— (1.02) 3,751.085=- (1.02)37 56,543.21=X

Last payment amount is $56,543.21.