Question4. Let's say you invest an amount now and leave it in the bank for 50 years.
WOULD YOU RATHER... - OPTION A - Invest $\$ 2000$ now, interest rate of $4 \%$ compounded annually

Studdy Solution

STEP 1

1. The principal amount invested is \$2000.
2. The interest rate is 4% compounded annually.
3. The investment period is 50 years.
4. We are using the formula for compound interest to calculate the future value of the investment.

STEP 2

1. Identify the formula for compound interest.
2. Substitute the given values into the formula.
3. Calculate the future value of the investment.

STEP 3

The formula for compound interest is given by:
$A = P \left(1 + \frac{r}{n}\right)^{nt}$
where: - $A$ is the amount of money accumulated after n years, including interest. - $P$ is the principal amount (initial investment). - $r$ is the annual interest rate (decimal). - $n$ is the number of times that interest is compounded per year. - $t$ is the time the money is invested for in years.

STEP 4

Substitute the given values into the compound interest formula:
- $P = 2000$ - $r = 0.04$ (since 4% is 0.04 as a decimal) - $n = 1$ (compounded annually) - $t = 50$
The formula becomes:
$A = 2000 \left(1 + \frac{0.04}{1}\right)^{1 \times 50}$

STEP 5

Calculate the future value of the investment:
$A = 2000 \left(1 + 0.04\right)^{50}$
$A = 2000 \times (1.04)^{50}$
Using a calculator, compute $(1.04)^{50}$ :
$(1.04)^{50} \approx 7.106$
Now, calculate $A$ :
$A = 2000 \times 7.106$
$A \approx 14212$
The future value of the investment is approximately \$14,212.
The future value of the investment is:
$\boxed{14212}$

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