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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 :

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

In both the cases, an individual would reach his target of reaching $1 million in savings.

What is savings?

Saving is that part of income which is not spent, or postponed consumption. Methods of saving include putting money aside in.

Example:

A deposit account, an investment fund, or as cash. Saving also regards cut back expenditures, such as recurring costs.

Computation of Savings:

(1). If starting at the age of 29 years, the total amount of saving would be:

Given that,

A= Annuity = $11,793,

n = time =  31 years,

r = Rate = 6%.

Now, we have to put here the formula of future value(FV):

[tex]\text{FV} =A \dfrac{(1+i)^n-1}{i}\\\\\\\text{FV} =\$11,793\times \dfrac{(1+6\%)^3^1-1}{6\%}\\\\\\\text{FV} = \$1,000,066.18[/tex]

(2). If starting at the age of 40 years, the total amount of saving would be:

Given that,

A= Annuity = $27,186,

n = time = 20 years,

r = Rate = 6%.

Here also, we have to put here the formula of future value(FV):

[tex]\text{FV} =A \dfrac{(1+i)^n-1}{i}\\\\\\\text{FV} =\$27,186\times \dfrac{(1+6\%)^2^0-1}{6\%}\\\\\\\text{FV} = \$1,000,053.1[/tex]

Learn more about savings, refer:

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