To find out how much money should be invested to achieve $10,000 in 3 years at an 8% annual interest rate compounded quarterly, you can use the compound interest formula:
P = A / (1 + r/n)^(nt)
Where:
P = principal amount (initial investment)
A = 10,000 (final amount desired)
r = 0.08 (annual interest rate as a decimal)
n = 4 (number of compounding periods per year, quarterly)
t = 3 (number of years)
Rearranging the formula to solve for P:
P = 10,000 / (1 + 0.08/4)^(4*3)
Using this formula, calculate P as follows:
P = 10,000 / (1 + 0.02)^(12)
P = 10,000 / (1.02)^12
P = 10,000 / 1.26824
Finally, compute P:
P = 7885.82
This means you should invest approximately $7,885.82 to have $10,000 in three years, with the interest compounded quarterly at 8% annually.
