I've done this problem at least 20 times a number of different ways, but I can't seem to get the correct answer. Please show all work and describe the EXACT formula you used:
Find the present value of the ordinary annuity: Payments of $78 are made quarterly for 10 years at 8% compounded quarterly.
Answer: $2133.73
Thanks!
I used the formula PV = A(i)/1-(1+(i)^-nt) as directed by my teacher, but it still isn't coming out correctly.
Let's go through the basics. You are receiving an annuity of $\$78$ each quarter for $40$ quarters. The interest rate is $8\%$ compounded quarterly, which is $2\%$ effective quarterly. Let $P_i$ denote the present value of the $i^{th}$ payment.
$P_1 = P(1+i)^{-1} = 78(1.02)^{-1}$
$P_2 = P(1+i)^{-2} = 78(1.02)^{-2}$
...
$P_{40} = P(1+i)^{-40} = 78(1.02)^{-40}$
The present value of the annuity is the sum of the above payments.
$\sum_{i = 1}^{40} P_i = 78\sum_{i = 1}^{40} (\frac{1}{1.02})^i = \frac{78}{1.02}\sum_{i = 0}^{39} (\frac{1}{1.02})^i = \frac{78}{1.02}\frac{1 - \frac{1}{(1.02)^{40}}}{1-\frac{1}{1.02}}$
where the $2^{\mathrm{nd}}$ equality is just to rewrite the series as the familiar geometric series and the final equality is applying the closed form solution for a geometric series solution.
Again, I'd recommend trying to understand the steps of the solution so you can understand why there is a formula for such equations and what it is, otherwise you can be led astray by wrong formulas (or even misusing correct formulas).