Amelia puts $1,000.00 into an account to use for school expenses. The account earns 2% interest, compounded annually. How much will be in the account after 7 years?

Question

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.

Answer 1

To calculate the amount in the account after 7 years using the formula for compound interest, we can use the following values:

• \( P = 1000.00 \) (the principal)
• \( r = 0.02 \) (the interest rate expressed as a decimal, which is 2%)
• \( n = 1 \) (the interest is compounded annually, meaning once per year)
• \( t = 7 \) (the time in years)

The compound interest formula is:

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

Plugging in the values:

\[ A = 1000 \left(1 + \frac{0.02}{1}\right)^{1 \cdot 7} \]

This simplifies to:

\[ A = 1000 \left(1 + 0.02\right)^{7} \]

\[ A = 1000 \left(1.02\right)^{7} \]

Now we calculate \( (1.02)^{7} \):

\[ (1.02)^{7} \approx 1.14869 \]

Now, substituting this back into the equation for \( A \):

\[ A \approx 1000 \times 1.14869 \approx 1148.69 \]

So, after rounding to the nearest cent, the amount in the account after 7 years will be:

\[ \boxed{1148.69} \]