Bridget puts $1,562.00 into an account to use for school expenses. The account earns 13.49% interest, compounded quarterly. How much will be in the account after 10 years?
Use the formula A=P1+
r
n
nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.
$


To solve this problem, we will use the compound interest formula:

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

Where:
- $ A $ is the amount of money in the account after interest.
- $ P $ is the principal, or the initial amount, which is \$1562.00.
- $ r $ is the annual interest rate as a decimal, which is 13.49% or 0.1349.
- $ n $ is the number of times the interest is compounded per year (quarterly, so $ n = 4 $).
- $ t $ is the time in years, which is 10 years.

Now, substitute these values into the formula:

\[
A = 1562 \left(1 + \frac{0.1349}{4}\right)^{4 \times 10}
\]

Let's calculate this step-by-step.The amount in the account after 10 years will be approximately **$5,886.83**.

Would you like more details or have any questions?

Here are 5 related questions you can explore:
1. How would the final amount change if the interest were compounded monthly instead of quarterly?
2. What if Bridget withdrew $500 after 5 years? How would that affect the final balance?
3. What would happen to the final amount if the interest rate was reduced to 10%?
4. How much total interest is earned in this scenario?
5. How would the calculation differ if the interest was compounded continuously?

**Tip**: The more frequently interest is compounded, the greater the effect on the final amount!

Bridget puts $1,562.00 into an account to use for school expenses. The account earns 13.49% interest, compounded quarterly. How much will be in the account after 10 years? Use the formula A=P(1+r/n)^(nt), where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. Round your answer to the nearest cent.

Calculate the final balance of an account earning 13.49% interest, compounded quarterly, after 10 years. Using the compound interest formula A = P(1 + r/n)^(nt), learn how Bridget's $1,562.00 grows to approximately $5,886.83. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation