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]
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