Questions: You deposit 4000 in an account earning 2% interest compounded monthly. How much will you have in the account in 15 years? Round to the nearest penny.

You deposit 4000 in an account earning 2% interest compounded monthly. How much will you have in the account in 15 years?

Round to the nearest penny.

Transcript text: You deposit $\$ 4000$ in an account earning $2 \%$ interest compounded monthly. How much will you have in the account in 15 years? Round to the nearest penny. $\square$

Solution

Solution Steps

Step 1: Convert the annual interest rate from a percentage to a decimal

The annual interest rate $r$ as a decimal is 0.02.

Step 2: Determine the number of times interest is compounded per year ($n$)

The interest is compounded 12 times per year.

Step 3: Identify the time period in years ($t$) for which the investment grows

The time period of the investment is 15 years.

Step 4: Substitute these values into the compound interest formula

Using the formula $A = P(1 + \frac{r}{n})^{nt}$, where $P$ is 4000, $r$ is 0.02, $n$ is 12, and $t$ is 15, we calculate the future value.

Step 5: Calculate the result to find the accumulated amount $A$ after $t$ years, including interest

The future value of the investment, rounded to 2 decimal places, is $5398.09.

Final Answer:

The accumulated amount after 15 years is $5398.09.

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