Question

You deposit $200 every quarter for 12 years into a sinking fund that pays 2.25% interest compounded annually. What is the future value of your fund?

Answer 1

Answer:

$16,974.57

Step-by-step explanation:

The formula for future value  is given by

$FV=PMT\frac{(1+i)^{n}-1}{i}$

where

FV = future value

PMT = amount deposited each period and is given as 200

i = rate per period = r/m where r is the interest rate and m the frequency of compounding. Here it is mentioned that r = 2.25% and interest is compounded annually ie once per year so m = 1

i = 2.25%/1 = 2.25% = 2.25/100 = 0.0225

The number of payments n = 48 since we make quarterly payments (4 per year) and we are asked to compute for 12 years

Plugging these values into the formula gives

$FV=200\frac{(1+0.0225)^{48}-1}{0.0225}$

which evaluates to

$16,974.57 which can be rounded up to $16975

depending on the accuracy you desire