Answer:
$36696.49
Explanation:
The formula for compound interest is given by:
A = P(1 + r / n)^nt
where:
A is the future value of the investment (in this case, $72,000),
P is the principal amount (the initial investment),
r is the annual interest rate (in decimal form),
n is the number of times interest is compounded per year, and
t is the number of years.
In your case, you want to find the principal amount (P). Rearranging the formula to solve for P, we get:
P = A / (1 + rn)^nt
Now, plug in the values:
P = 72000 / (1 + 0.08 / 12)^12×10
Let's calculate this value:
P = 72000 / (1 + 0.0066667)^120
P ≈ 72000 / (1.0066667)^120
P ≈ 72000 / 1.962359
P ≈ 36696.49
Therefore, the lump sum that must be invested at 8% compounded monthly for the investment to grow to $72,000 in 10 years is approximately $36696.49.