Question

A bank offers a 7% interest rate compounded two times per year on new savings deposits. If a customer deposits $100.00 in the account, how much will be in the account in total after 5 years? Round to the nearest dollar.(1 point)
$

Answer 1

To calculate the total amount in the account after 5 years with compound interest, we can use the formula for compound interest:

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

where:
- \(A\) = the amount of money accumulated after n years, including interest.
- \(P\) = the principal amount (the initial deposit).
- \(r\) = the annual interest rate (decimal).
- \(n\) = the number of times that interest is compounded per year.
- \(t\) = the number of years the money is invested or borrowed.

Given:
- \(P = 100\) (the initial deposit)
- \(r = 0.07\) (the interest rate of 7%)
- \(n = 2\) (since interest is compounded twice a year)
- \(t = 5\) (the number of years)

Now, let's plug in these values into the formula:

\[
A = 100 \left(1 + \frac{0.07}{2}\right)^{2 \times 5}
\]

Calculating the components:

1. Calculate \(\frac{0.07}{2} = 0.035\).
2. Then calculate \(1 + 0.035 = 1.035\).
3. Calculate \(nt = 2 \times 5 = 10\).
4. Now raise \(1.035\) to the power of \(10\):

\[
1.035^{10} \approx 1.4106
\]

5. Finally, multiply by the principal amount:

\[
A \approx 100 \times 1.4106 \approx 141.06
\]

Rounding to the nearest dollar, the total amount in the account after 5 years will be approximately:

\[
\text{\$141}
\]

So, the answer is:

\[
\boxed{141}
\]