Final answer:
Donna invested $1,200 at a 7% annual interest rate for 3 years. The future value of her investment is calculated using the formula for compound interest, which involves multiplying the principal amount by the growth factor raised to the power of the number of years.
Step-by-step explanation:
The subject of this question is the calculation of the future value of an investment made at a fixed interest rate for a certain number of years, which falls under the category of compound interest. Donna invested $1,200 at a 7% annual interest rate for 3 years. To calculate the value of the investment at the end of the period, we use the compound interest formula:
FV = P(1 + r)^n
Where:
- FV stands for Future Value,
- P stands for the principal amount (initial investment),
- r stands for the annual interest rate (in decimal form), and
- n stands for the number of years.
In this case, P = $1,200, r = 0.07 (since 7% = 0.07 as a decimal), and n = 3 years.
Substitute the values into the formula:
FV = $1,200(1 + 0.07)^3
Calculate the future value step by step:
Calculate the growth factor: (1 + 0.07) = 1.07,
Raise the growth factor to the power of 3: 1.07^3,
Multiply the principal amount by the result of step 2: $1,200 × (result of step 2).
This results in the future value of Donna's investment after 3 years.