Final answer:
Stacey's investment of $3,800 at 4.5% interest compounded monthly for 7 years will grow to approximately $5,527.04.
Step-by-step explanation:
Compound Interest Calculation
To calculate the future value of an investment with compound interest, we use the formula:
FV = P(1 + r/n)^(nt)
Where:
- FV is the future value of the investment,
- P is the principal amount (the initial amount of money),
- r is the annual interest rate (decimal),
- n is the number of times that interest is compounded per year,
- t is the time the money is invested or borrowed for, in years.
Applying this to Stacey's investment:
- P = $3,800
- r = 4.5% or 0.045 (as a decimal)
- n = 12 (since the interest is compounded monthly)
- t = 7 years
We get:
FV = $3,800(1 + 0.045/12)^(12*7)
Calculating the above expression gives us the future value of Stacey's investment after 7 years. It's important to remember to convert the interest rate to a decimal by dividing by 100.
By using a scientific calculator or financial calculator, we perform the following operations:
First, divide the annual rate by the number of compounding periods per year:
0.045 / 12 = 0.00375
Add 1 to this result:
1 + 0.00375 = 1.00375
Now, raise this sum to the power of the total number of compounding periods:
(1.00375)^(12*7) = (1.00375)^84
Lastly, multiply this by the principal amount:
$3,800 * (1.00375)^84 = $5,527.04
The investment will grow to approximately $5,527.04 after 7 years, assuming it is compounded monthly at an annual interest rate of 4.5%.