Question

Here is your 25-year savings plan:

• $3,600 each year for the next two years. You will earn just 2.0% interest, or return, on this savings.
• $6,000 per year for years 3, 4, and 5. Because you will have learned to be a smart beginning investor by this time, you believe you can earn a 6.0% annual return on any invested funds.
• $12,000 per year for the remaining 20 years. By this time you expect to earn a 12.0% annual return.

If you never withdraw any funds from the account, if all funds earn the going rate of return for the time period, and if all of your savings is deposited at the end of each year, how much should you have in total at the end of 25 years?

Answer 1

From Year 1 to Year 2

Annual Deposit = $3,600

Interest Rate = 2%

Calculating Value at the end of Year 2,

Using TVM Calculation,

Value = [PV = 0, T = 2, PMT = 3600, I = 0.02]

Value = $7,272

From Year 3 to Year 5,

Annual Deposit = $6,000

Interest Rate = 6%

Calculating Value at the end of Year 5,

Using TVM Calculation,

Value = [PV = 7272, PMT = 6000, T = 3, I = 0.06]

Value = $27,762.67

From Year 11 to Year 25

Annual Deposit = $12,000

Interest Rate = 12%

Value at the end of Year 25,

Using TVM Calculation,

Future Value = [PV = 27762.67, PMT = 12000, T = 20, I = 0.12]

Future Value = $1,132,436.16

So,

Future Value at the end of Year 25 = $1,132,436.16