Question

7900 dollars is placed in an account with an annual interest rate of 5.5%. how much will be in the account after 11 years, to the nearest cent?

Explanation:

Step1: Identify the formula for compound interest

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where:

• $A$ is the amount of money accumulated after $n$ years, including interest.
• $P$ is the principal amount (the initial amount of money).
• $r$ 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.

Assuming the interest is compounded annually, $n = 1$.

Step2: Convert the interest rate to decimal

The annual interest rate $r = 5.5\% = 0.055$.

Step3: Substitute the values into the formula

We have $P = 7900$, $r = 0.055$, $n = 1$, and $t = 11$.

Substituting these values into the formula:

$$
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$$

Step4: Calculate $(1.055)^{11}$

First, calculate $(1.055)^{11}$. Using a calculator, $(1.055)^{11}\approx1.795856$.

Step5: Calculate the amount $A$

Multiply this by the principal amount:

$$ A = 7900\times1.795856\approx14187.26 $$

Answer:

The amount in the account after 11 years, to the nearest cent, is $\$14187.26$.