Final answer:
To find out how long it will take for Aldo to have enough money for his project, we use the formula for compound interest: A = P(1 + r/n)^(nt). Plugging in the given values, we find that it will take approximately 3.36 years.
Step-by-step explanation:
To find out how long it will take for Aldo to have enough money for his project, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the final amount of money Aldo will have
- P is the principal amount he invests initially
- r is the annual interest rate (as a decimal)
- n is the number of times the interest is compounded per year
- t is the number of years
In this case, Aldo invests $4000, the interest rate is 10.2%, compounded monthly (n=12), and he needs $4984. Plugging these values into the formula, we get:
$4984 = $4000(1 + 0.102/12)^(12t)
Solve for t:
$4984/$4000 = (1 + 0.102/12)^(12t)
Taking the natural logarithm of both sides to solve for t:
t = (ln($4984/$4000))/(12*ln(1 + 0.102/12))
Using a calculator, t ≈ 3.36 years.