Question

You need $20,000 and you think you could earn an annual rate of 7%. If you plan to make deposit of $300 per month, how long before reach your goal? (Assume the first payment is made 1 month.)

Answer 1

$300 per month depositing would be an annuity.

We need $ 20k at the foreseable date.

We need to find out at what time, the future value of this annuity would equal the desired amount. (I.e Rs 20k)

The future value of an annuity in case payment is one period away is : P((1+r^n)-1)/r,
where r is the rate of interest.

Calculating monthly,
R is 7/1200,
Future Value is $20000
P is $ 300
We need to find n.

Now,
Recalculating the equation,
20000 = 300 ((1+7/1200)^n)-1) / (7/1200)

or,

20000/300*1200/7 = ((1+7/1200)-^n)-1
or,
(1+7/1200)^n = 11429.57
Using Logarithms,
n = 1607 months (approx)