To determine the principal P that must be invested at a rate r = 7%, compounded monthly, to reach $500,000 in t = 17 years, we can use the formula for compound interest:
A = P (1 + r/n)^(nt)
Where:
- A is the amount accumulated after t years
- P is the principal amount (initial investment)
- r is the annual interest rate (as a decimal)
- n is the number of times interest is compounded per year
- t is the time the money is invested for, in years
Given A = $500,000, r = 0.07 (7% as a decimal), n = 12 (compounded monthly), and t = 17, we can solve for P:
500,000 = P (1 + 0.07/12)^(12*17)
500,000 = P (1 + 0.07/12)^204
P = 500,000 / (1 + 0.07/12)^204
Calculating this value will give us the principal amount P. Let's compute it.
