Question

How much money should be invested every month with 8% interest per year compounded monthly in order to save up $10,000 in 15 months?

Answer 1

$ 637.17

Explanation:

First, let's convert the interest per year (iy) to interest per month (im):

(1 + im)¹² = 1 + iy

(1 + im)¹² = 1 + 0.08

1 + im =
`1.08^(1/12)`

1 + im = 1.00643

im = 0.00643

im = 0.643%

The total amount (A) of an investment is:

`A = R*(((1+im)^(n)-1)/(im))`

Where R is the amount invested per month, and n the number of monthes. So:

`10,000 = R*(((1.00643)^(15)-1)/(0.00643) )`

10,000 = R*15.6943

R = $ 637.17