Given:
A = $950
n = every quarter = 4 times a year
time = 6 years and 6 months = 6.5 years
rate = 5% = 0.05
Let's find the accumulated amount and the present value.
For the accumulated amount, apply the formula:
[tex]F=A(\frac{(1+i)^{n+1}-1}{i}-1)[/tex]We have:
[tex]\begin{gathered} F=950(\frac{(1+\frac{0.05}{4})^{4*6.5+1}-1}{\frac{0.05}{4}}-1_) \\ \\ F=950(\frac{0.3812}{0.0125}-1) \\ \\ F=29336 \end{gathered}[/tex]The accumulated value is $29,336
• (b,). The present value.
Apply the formula:
[tex]P=A(\frac{1-(1+i)^{-n+1}}{i}+1)[/tex]We have:
[tex]\begin{gathered} P=950(\frac{1-(1+\frac{0.05}{4})^{-6.5*4+1}}{\frac{0.05}{4}}+1) \\ \\ P=950(\frac{0.2669658582}{0.0125}+1) \\ \\ P=950(22.35726866) \\ \\ P=21239.41 \end{gathered}[/tex]The present value is $21239.41
ANSWER:
• Accumulated amount, F = $29,336
• Present value, P = $21239.41
