Math Snap

STEP 1

Assumptions1. The principal amount is $6000. The annual interest rate is4%
3. The time for compounding is5 years4. The interest is compounded semiannually

STEP 2

The formula for compound interest is given by$$A = \left(1 + \frac{r}{n}\right)^{nt}$$where- A is the amount of money accumulated after n years, including interest.
- is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.

STEP 3

First, we need to convert the annual interest rate from a percentage to a decimal. We do this by dividing the percentage by100.
$$r = \frac{\%}{100} =0.04$$

STEP 4

Now, we need to identify the number of times the interest is compounded per year. Since it is compounded semiannually, this means it is compounded twice a year.
$$n =2$$

STEP 5

Substitute the values of, r, n and t into the formula.
A = \($\)6000 \left(1 + \frac{0.04}{2}\right)^{2 \times5}

STEP 6

Calculate the amount in the account after5 years.
A = \($\)6000 \left(1 +0.02\right)^{10}

STEP 7

implify the expression inside the parentheses.
A = \($\)6000 \times (1.02)^{10}

Calculate the final amount.
A = \($\)6000 \times (1.02)^{10} = \($\)7298.63The amount in the account after5 years if the account is compounded semiannually is $7298.63.