Answer:
$13,992.14
Step-by-step explanation:
To calculate the amount of each annuity deposited every six months for six years at a 5.5% interest rate compounded semi-annually, we can use the formula for the future value of an ordinary annuity:
[tex]FV=\dfrac{PMT\left(\left(1+\dfrac{r}{n}\right)^{nt} - 1\right)}{\dfrac{r}{n}}[/tex]
where:
- FV = Future Value
- PMT = Payment Amount
- r = interest rate in decimal form
- n = number of periods per year
- t = number of years
Substitute the values into the formula and solve for FV:
[tex]FV=\dfrac{1000\left(\left(1+\dfrac{0.055}{2}\right)^{2\cdot 6} - 1\right)}{\dfrac{0.055}{2}}\\\\\\\\FV=\dfrac{1000\left(\left(1.0275\right)^{12} - 1\right)}{0.0275}\\\\\\\\FV=13992.1372899...\\\\\\FV=\$13992.14[/tex]
So, each annuity of $1000 deposited every six months for six years at 5.5% compounded semi-annually will amount to approximately $13,992.14.
