Final answer:
The value of Theo's investment in 4 years is approximately $7,576.80.
Step-by-step explanation:
To determine the value of Theo's investment in 4 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the future value of the investment
- 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 number of years
Given that Theo invested $6600 at an interest rate of 4.5% compounded monthly, we have:
- P = $6600
- r = 4.5% = 0.045
- n = 12 (compounded monthly)
- t = 4 years
Plugging in the values, we can calculate the future value:
- A = 6600(1 + 0.045/12)^(12*4)
- A = 6600(1 + 0.00375)^(48)
- A = 6600(1.00375)^(48)
- A ≈ $7,576.80
The value of Theo's investment in 4 years is approximately $7,576.80.