If 42600 dollars is invested at an interest rate of 5 percent per year, compounded semiannually.
What does semiannually mean? to find the values at 5 years would you just multiply?
Semiannually means that interest is paid and compounded every six months. The amount added on is 2.5% (1/2 of 5%) each time.
To get the value after five years, multiply by (1.025)^10 = 1.2800845. Note that that is more than 1.25 you would get by not compounding.
You end up with
$53,531.60. That might be a few cents off, depending upon how pennies get rounded off each time.
"Semiannually" means that the interest is compounded twice a year. In other words, the investment's value will be recalculated and the interest will be added to the investment balance every six months.
To find the value of the investment after 5 years, you would need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of the investment after t years
P = the initial investment amount
r = the annual interest rate
n = the number of compounding periods per year
t = the number of years
In this case, the initial investment amount is $42,600, the annual interest rate is 5% (or 0.05), and the compounding period is semiannually (twice a year). Therefore, n = 2.
Plugging the values into the formula, you would have:
A = $42,600 * (1 + 0.05/2)^(2 * 5)
To calculate this, you would need to perform the following steps:
1. Divide the annual interest rate by the number of compounding periods per year: 0.05/2 = 0.025.
2. Multiply the number of compounding periods per year by the number of years: 2 * 5 = 10.
3. Add 1 to the result from step 1: 1 + 0.025 = 1.025.
4. Raise the result from step 3 to the power of the result from step 2: 1.025^10.
5. Multiply the initial investment amount by the result from step 4 to find the final amount.
By following these steps, you can find the value of the investment after 5 years.