# Amount of an Ordinary Annuity

• Dec 19th 2006, 06:41 PM
asiankatt
Amount of an Ordinary Annuity
Hi there.

I've been trying a few questions for quite sometime and haven't been able to get to the correct answer.

I would apperciate it if you could show me how to derive to the answer.

Find the amount of each ordinary annuity.
a. a payment of $1500 at the end of every 3 months at 8% per annum, compounded quarterly. b. a payment of$700 at the end of every month, into an account that pays 10% per annum, compounded monthly.

c. a payment of $2800 at the end of every 6 months for 5 years with an interest rate of 9% per annum, compounded semi-annually. Thanks so much in advance :) • Dec 19th 2006, 07:09 PM Soroban Hello, asiankatt! There is a formula for these problems . . . . . .$\displaystyle \boxed{A \;=\;D\,\frac{(1+i)^n - 1}{i}}$where: .$\displaystyle \begin{Bmatrix}A & = & \text{final amount} \\ D & = & \text{periodic deposit} \\ i & = & \text{periodic interest rate} \\ n & = & \text{number of periods}\end{Bmatrix} $I'll do the third one for you. For the others, we need to be told the number of years. Quote: Find the amount of each ordinary annuity. c. A payment of$2800 at the end of every 6 months for 5 years
with an interest rate of 9% per annum, compounded semi-annually.

We are given: .$\displaystyle \begin{Bmatrix}D \,= \,2800 \\ i \, = \,\frac{9\%}{2} \,=\,0.045 \\ n = 2\!\cdot\!5\,=\,10\end{Bmatrix}$

Therefore: .$\displaystyle A \;=\;2800\,\frac{(1.045)^{10} - 1}{0.045} \:\approx\:\$34,406.99\$