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)

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1 answer

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 \(10\):

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

  1. 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:

\[ \boxed{141} \]