Question

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.

Answer 1

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:

`F=A(((1+i)^(n+1)-1)/(i)-1)`

We have:

`\begin{gathered} F=950(((1+(0.05)/(4))^(4*6.5+1)-1)/((0.05)/(4))-1_) \\ \\ F=950((0.3812)/(0.0125)-1) \\ \\ F=29336 \end{gathered}`

The accumulated value is $29,336

• (b,). The present value.

Apply the formula:

`P=A((1-(1+i)^(-n+1))/(i)+1)`

We have:

`\begin{gathered} P=950((1-(1+(0.05)/(4))^(-6.5*4+1))/((0.05)/(4))+1) \\ \\ P=950((0.2669658582)/(0.0125)+1) \\ \\ P=950(22.35726866) \\ \\ P=21239.41 \end{gathered}`

The present value is $21239.41

ANSWER:

• Accumulated amount, F = $29,336

• Present value, P = $21239.41