Answer:
$80,468.23
Step-by-step explanation:
To find the future value of the account where equal payments are made at the beginning of each period for a specified number of periods, we can use the Future Value of an Annuity Due formula:
[tex]FV=PMT\left[\dfrac{\left(\left(1+\dfrac{r}{n}\right)^{nt}-1\right)\left(1+\dfrac{r}{n}\right)}{\dfrac{r}{n}}\right][/tex]
where:
- FV = Future Value
- PMT = Payment Amount
- r = interest rate per year (decimal form)
- n = number of times interest is applied per year
- t = time in years
In this case:
- PMT = $900
- r = 8% = 0.08
- n = 2 (semi-annually)
- t = 19 years
Substitute the given values into the formula and solve for FV:
[tex]FV=900\left[\dfrac{\left(\left(1+\dfrac{0.08}{2}\right)^{2 \cdot 19}-1\right)\left(1+\dfrac{0.08}{2}\right)}{\dfrac{0.08}{2}}\right]\\\\\\\\FV=900\left[\dfrac{\left(\left(1.04\right)^{38}-1\right)(1.04)}{0.04}\right]\\\\\\\\FV=80468.2347...\\\\\\FV=\$80,468.23\; \sf (nearest\;tenth)[/tex]
Therefore, the future value of the account rounded to the nearest cent is:
[tex]\Large\boxed{\boxed{\$80,468.23}}[/tex]
