Question

You are advising a co-worker on saving for retirement. The co-worker gives you two possible scenarios:

Scenario 1: Suppose you invest $170 a month for 6 years into an account earning 10% compounded monthly. After 6 years, you leave the money, without making additional deposits, in the account for another 22 years. How much will you have in the end?

Scenario 2: Suppose instead you didn't invest anything for the first 6 years, then deposited $170 a month for 22 years into an account earning 10% compounded monthly. How much will you have in the end?

Include the following in a report.

• What is the future value of each scenario?
• What is the total amount invested for each scenario?
• What is the total interest earned for each investment?
• How many more monthly deposits would you need to make for the first scenario to have the same future value as the second scenario?
• How many more monthly deposits would you need to make for the second scenario to have the same total interest as the second scenario?

Answer 1

Scenario 1: PMT = 170; N = 6*12 = 72; rate = 10%/12 = 0.833%, CPT FV. FV (after 6 years) = 16,678.92

This amount for invested is another 22 years: PV = 16,678.92; N = 22; rate = 10%, CPT FV. FV (after 28 years) = 135,771.02

Scenario 2: PMT = 170; N = 22*12 = 264; rate = 10%/12 = 0.833%, CPT FV. FV = 162,039.54

1). Future value of scenario 1 = 135,771.02; Future value of scenario 2 = 162,039.54

2). Total amount invested for scenario 1 = monthly payment*number of payments = 170*72 = 12,240

Total amount invested for scenario 2 = monthly payment*number of payments = 170*264 = 44,880

3). Total interest earned for scenario 1 = FV - amount invested = 135,771.02 - 12,240 = 123,531.02

Total interest earned for scenario 1 = FV - amount invested = 162,039.54 - 44,880 = 117,159.54

4). To compute the number of payments which will make the FV in scenario 1 equal to the FV in scenario 2, we will use Solver, as follows:

Currently, in scenario 1, 72 payments are made. To match the FV of scenario 2, 92 payments have to be made, so extra payments needed are 92 - 72 = 20

5). Again, we can solve this using Solver, as follows:

264 payments are made in scenario 2. If it is increased to 269 then it will have the same interest earned as scenario 1.

Extra payments needed = 269 - 264 = 5.