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

Answer:

$ 637.17

Step-by-step 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:

$A = R*(\frac{(1+im)^{n}-1}{im})$

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

$10,000 = R*(\frac{(1.00643)^{15}-1}{0.00643} )$

10,000 = R*15.6943

R = $ 637.17