Question

Jackson had agreed to make two payments. He planned to make a payment of $2600 due in sixteen months and a payment of $2400 in two years. Instead of the original payment plan, if Jackson makes a payment of $3200 now, when should he make a second payment of $2900 if money is worth 8.5% compounded semi annually?

Please upload a full solution using the Equivalent Values Approach

Answer 1

The first part is to calculate the present value of payments made as per the original plan using the steps in the below mentioned screenshot

Finding the time of the second payment in Plan 2 to make sum of present value equal to sum of present value in original plan.

Present Value = Payment 1/ (1+semi annual int%)^semi annual period + Payment 2/ (1+semi annual int%)^semi annual period

4358.78 = 3200 / (1.0425)^0 + 2900 / (1.0425)^N

4358.78 = 3200 + 2900 / (1.0425)^N

1158.78 = 2900 / (1.0425)^N

(1.0425)^N = 2900 / 1158.78

(1.0425)^N = 2.502

Taing log on both sides

Log (1.0425)^N = Log (2.502)

N*(Log(1.0425)) = Log (2.502)

N =  Log (2.502) /  Log(1.0425)

N = 22.034

semi annual period = 22.034

Month = semi annual period * 6

Month = 22.034 * 6

Month = 132.204 (Rounding off to 132)

Hence, we can make the second payment in 132nd month to have the same present value as Original Plan. We can also write this as "the second payment can be made in 11th year to have the same present value as Original Plan."

(132 months / 12=11 years)