Question

Find the future value of an annuity if you invest $850 quarterly for 5 years at 1.5% compounded quarterly.

Answer 1

Basic Principles. Define the building blocks and write ti down.

i = 0.015 -- The annual percentage rate. It is given in the problem statement.
j = i/4 = 0.00375 -- The quarterly percentage rate
r = 1+j = 1.00375 -- The Quarterly Accumulation Factor.

$1 invested now will be $1 * r = $1.015 in 3 months. Now build.

\( 850⋅(r^{20}+r^{19}+r^{18}+...+r)=850⋅\dfrac{r^{21}−r}{j}\)

No need to wonder which formula to use. Define what you need and BUILD IT!

Answer 2

Interest = (1 + .015/4)^4
Interest = 1.00375^4
Interest = 1.0150845861
Interest = 1.50845861%

Annuity Value
Here's the Annuity Formula

Answer 3

We know that $3,400 is being invested per year so
3,400 * [((1.0150845861)^6 -1) / .0150845861] - 3,400
3,400 * (.0939901174 /.0150845861) -3,400
3,400 * (6.2308714854) -3,400
21,184.96 -3,400 =
17,784.96

See? It's just that simple!

Answer 4

After all that, it is still not an exact answer.
The formula I posted (and used) is for an annuity which has amounts added annually.
I should have used a quarterly annuity formula - but I couldn't locate one.
Anyway, that answer should be close enough.

Answer 5

$17,685.54

That is as exact as possibly to the penny and is based on the exact quarterly formula given above.