Question Cynthia invested $$ \$ 12,000 $$ in a savings account. If the interest rate is $$ 6 \% $$ per year, how much will be in the account in 10 years for quarterly compounding? Round your answer to two decimal places. Provide your answer below:

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UpStudy AI · Accepted Answer

To calculate the future value of an investment with quarterly compounding interest, we can use the formula:

$$
A = P \left(1 + \frac{r}{n}\right)^{nt}
$$

where:
- $$ A $$ is the amount of money accumulated after n years, including interest.
- $$ P $$ is the principal amount (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 number of years the money is invested or borrowed.

Given:
- $$ P = 12000 $$
- $$ r = 0.06 $$ (6% as a decimal)
- $$ n = 4 $$ (quarterly compounding)
- $$ t = 10 $$

Now, we can plug in the values:

$$
A = 12000 \left(1 + \frac{0.06}{4}\right)^{4 \times 10}
$$

Calculating $$ \frac{0.06}{4} $$:

$$
\frac{0.06}{4} = 0.015
$$

Now, substituting this back into the formula:

$$
A = 12000 \left(1 + 0.015\right)^{40}
$$

Calculating $$ 1 + 0.015 $$:

$$
1 + 0.015 = 1.015
$$

Now we raise $$ 1.015 $$ to the power of $$ 40 $$:

$$
1.015^{40} \approx 1.80611123467
$$

Now, we multiply this by the principal amount:

$$
A \approx 12000 \times 1.80611123467 \approx 21673.334816
$$

Rounding to two decimal places:

$$
A \approx 21673.33
$$

Thus, the amount in the account after 10 years will be approximately **\$21,673.33**.
The amount in the account after 10 years will be approximately \$21,673.33.

Question
Cynthia invested in a savings account. If the interest rate is per year, how much will be in
the account in 10 years for quarterly compounding? Round your answer to two decimal places.
Provide your answer below:

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Question Cynthia invested in a savings account. If the interest rate is per year, how much will be in the account in 10 years for quarterly compounding? Round your answer to two decimal places. Provide your answer below: