Question

Gracie wants to buy a new hammer, and 5 years later, Gracie estimates the cost of the hammer would be $28,000. If she invests $12,000 now at a rate of 6% compounded semi-annually, how much does she miss her goal by

Answer 1

Gracie will miss her goal of saving $28,000 for a new hammer by investing $12,000 at a semi-annual 6% interest rate over 5 years by $11,877.12.

Step-by-step explanation:

To determine how much Gracie will miss her goal of $28,000 by if she invests $12,000 now at a rate of 6% compounded semi-annually, we use the formula for compound interest:

FV = PV * (1 + r/n)^(nt)
where:

• FV is the future value of the investment.
• PV is the present value or initial amount ($12,000).
• r is the annual interest rate (6% or 0.06).
• n is the number of times the interest is compounded per year (2 for semi-annually).
• t is the number of years the money is invested (5 years).

After calculating the future value, we subtract it from Gracie's goal to find the difference.

Using the formula:
FV = $12,000 * (1 + 0.06/2)^(2*5) = $16,122.88 approximately
Gracie will miss her goal by $28,000 - $16,122.88 = $11,877.12.