If an apartment complex will need painting in
3
1
2
years and the job will cost $25,000, what amount needs to be deposited into an account now in order to have the necessary funds? The account pays 12% interest compounded semiannually.
if you meant 3 1/2 years, then you will need
25000/(1+.12/2)^(2*3.5) = $16,626.43
To calculate the amount that needs to be deposited now, we need to determine the future value of the $25,000 when compounded with 12% interest semiannually over the given time frame.
First, let's convert the time to number of six-month periods. Since the painting needs to be done in 3, 1, and 2 years respectively, we have a total of 6 six-month periods.
Next, we can use the future value formula for compound interest:
Future Value = Present Value * (1 + (Rate / 2))^n
Where:
- Present Value is the amount needed to be deposited now
- Rate is the interest rate per six-month period (12% divided by 2, as interest is compounded semiannually)
- n is the number of six-month periods (6)
Substituting the given values into the formula:
$25,000 = Present Value * (1 + (0.12 / 2))^6
Let's now solve the equation step by step:
1. Simplify the rate calculation:
$25,000 = Present Value * (1 + 0.06)^6
2. Simplify the exponent:
$25,000 = Present Value * (1.06)^6
3. Calculate the future value:
$25,000 = Present Value * 1.41851
4. Rearrange the equation to solve for Present Value:
Present Value = $25,000 / 1.41851
Using a calculator, we can find that Present Value is approximately $17,623.39.
Therefore, to have the necessary funds to paint the apartment complex in the future, approximately $17,623.39 needs to be deposited into an account now.