Question

You have just made your first $4,500 contribution to your individual retirement account. Assume you earn a 10.55 percent rate of return and make no additional contributions.

Requirement 1:

What will your account be worth when you retire in 44 years? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Amount

$

Requirement 2:

What if you wait 10 years before contributing? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Amount

$

Answer 1

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

1.A=4500*(1.1055)^44

=$371,361.93(Approx).

2.A=4500*(1.1055)^34

=$136,210.29(Approx).

Answer 2

 Calculation :-

Requirement 1: Growing for 44 Years

You invest $4,500 today at an annual return of 10.55%. The formula for future value is:

$$\text{Future Value}=\text{Present Value}\times (1+\text{Interest Rate}{)}^{\text{Time}}$$

Plugging in the numbers:

$$\text{FV}=4500\times (1+0.1055{)}^{44}$$$$\text{FV}=4500\times (1.1055{)}^{44}$$

Using a calculator:

1. $1.1055^{44}\approx 89.49521$

2. Multiply by $4,500:

$$4500\times 89.49521=402,728.44$$

Amount ≈ $402,728.44

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Requirement 2: Waiting 10 Years, Then Investing for 34 Years

If you wait 10 years, you only have 34 years left to grow the money.

Using the same formula:

$$\text{FV}=4500\times (1.1055{)}^{34}$$

Calculating:

1. $1.1055^{34}\approx 32.54369$

2. Multiply by $4,500:

$$4500\times 32.54369=146,446.60$$

Amount ≈ $146,446.60