Question

Carol is depositing $1500 into an account earning 3% compounded semiannually. How much money will be in the account after 25 years?

Answer 1

$3157.86

Step-by-step explanation

We have that Carol is depositing $1500 into an account earning 3% that is compounded semiannually.

The formula for amount for a compound interest is:

`A\text{ = }P(1\text{ + }(r)/(n))^(n\cdot t)`

where P = principal (amount deposited)

r = interest rate

t = number of years

n = number of times interest is compounded

Since the interest is compounded twice a year (semiannually), n = 2.

From the question:

P = $1500

r = 3% = 0.03

t = 25 years

So, the amount of money that will be there after 25 years is:

`\begin{gathered} A\text{ = 1500(1 + }(0.03)/(2))^(2\cdot25) \\ A=1500(1+0.015)^(50) \\ \text{A = 1500(1.015)}^(50) \\ A\text{ = \$3157.86} \end{gathered}`