Answer:
$4,372.10
Step-by-step explanation:
To find the sinking fund payment that would need to be made at the end of each period for a specified number of periods, we can use the Future Value of an Ordinary Annuity formula:
[tex]FV=PMT\left[\dfrac{\left(\left(1+\dfrac{r}{t}\right)^{nt}-1\right)}{\dfrac{r}{t}}\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:
- FV = $29,000
- r = 8% = 0.08
- n = 2 (semi-annually)
- t = 3 years
Substitute the given values into the formula and solve for PMT:
[tex]29000=PMT\left[\dfrac{\left(\left(1+\dfrac{0.08}{2}\right)^{2 \cdot 3}-1\right)}{\dfrac{0.08}{2}}\right]\\\\\\\\29000=PMT\left[\dfrac{\left(\left(1.04\right)^{6}-1\right)}{0.04}\right]\\\\\\\\PMT=\dfrac{29000}{\left[\dfrac{\left(\left(1.04\right)^{6}-1\right)}{0.04}\right]}\\\\\\\\PMT=4,372.0951727...\\\\\\PMT=\$4,372.10\; \sf (nearest\;tenth)[/tex]
Therefore, the sinking fund payment rounded to the nearest cent is:
[tex]\Large\boxed{\boxed{\$4,372.10}}[/tex]
