Question

How much money will you need to invest initially to have $1,000,000.00 in 18 years if the money is compounded monthly at an annual rate of 3%?

$587,394.61


$582,761.18


$583,141.09


$583,923.63

Answer 1

`\$583,141.09`

Explanation:

The compound interest formula is equal to

`A=P(1+(r)/(n))^(nt)`

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

`t=18\ years\\ A=\$1,000,000.00\\ r=3\%=3/100=0.03\\n=12`

substitute in the formula above

`1,000,000=P(1+(0.03)/(12))^(12*18)`

Solve for P

`1,000,000=P(1.0025)^(216)`

`P=1,000,000/(1.0025)^(216)`

`P=\$583,141.09`