Question

Compound interest is a very powerful way to save for your retirement. Saving a little and giving it time to grow is often more effective than saving a lot over a short period of time. To illustrate​ this, suppose your goal is to save​ $1 million by the age of 67

What amount of money will be saved by socking away

​$3,759

per year starting at age

23

with

a

7​%

annual interest rate. Will you achieve your goal using the​ long-term savings​ plan? What amount of money will be saved by socking away

​$15,812

per year starting at age

42

at the same interest​ rate? Will you achieve your goal using the​ short-term savings​ plan?

Answer 1

Goal is to save $1,000,000 by the age of 67.

a. If the yearly deposit is $3,759 starting at the age of 23 with interest of 7%, what will be the Future Value at 67^th year?

Number of deposits = 45 years (23 to 67)

Future Value = $3,759 (F/A, 7%, 45)

Future Value = $3,759 (285.74931) = $1,074,131.65

Will you achieve the goal?

YES.

b. If the yearly deposit is $15,812 starting at the age of 42 with interest of 7%, what will be the Future Value at 67^th year?

Number of deposits = 26 years (42 to 67)

Future Value = $15,812 (F/A, 7%, 26)

Future Value = $15,812 (68.67647) = $1,085,912.34

Will you achieve the goal?

YES.