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4. Find the amount and the present value of an annuity due of P950 every quarter for 6years and 6 months, if money is worth 5% compounded quarterly.The formula is attached. I don’t know if my answer is right. That’s why I like to compare my answer to your answer.

4 Find the amount and the present value of an annuity due of P950 every quarter for 6years and 6 months if money is worth 5 compounded quarterlyThe formula is a class=

Respuesta :

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