To calculate how much Samiyah must invest per month, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (the monthly investment)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case, Samiyah wants to have $5,000,000 when she retires in 35 years, and expects to make a 17% interest rate. We'll assume interest is compounded annually (n = 1).
A = $5,000,000
r = 17% = 0.17
n = 1
t = 35
Substituting these values into the formula, we have:
$5,000,000 = P(1 + 0.17/1)^(1*35)
Simplifying the equation:
$5,000,000 = P(1.17)^35
Divide both sides of the equation by (1.17)^35 to solve for P:
P = $5,000,000 / (1.17)^35
P ≈ $243.26
Therefore, Samiyah must invest approximately $243.26 per month to have $5,000,000 when she retires in 35 years.
