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 6060. What amount of money will be saved by socking away ​$11 comma 79311,793 per year starting at age 2929 with aa 66​% annual interest rate. Will you achieve your goal using the​ long-term savings​ plan? What amount of money will be saved by socking away ​$27 comma 18627,186 per year starting at age 4040 at the same interest​ rate? Will you achieve your goal using the​ short-term savings​ plan?

Answer 1

Answer:

In both cases you will reach $1 million in savings

Explanation:

Giving the following information:

Suppose your goal is to save​ $1 million by the age of 60.

1) What amount of money will be saved by socking away ​$11,793 per year starting at age 29 with a 6​% annual interest rate?

We need to use the final value formula with an annual deposit:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

FV= {11793*[(1.06^31)-1]}/0.06= $1,000,066.18

2)What amount of money will be saved by socking away ​$27,186 per year starting at age 40 at the same interest​ rate?

FV= {27186*[(1.06^20)-1]}/0.06

FV= $1,000,053.1