Final answer:
The value of Evan's investment after three years with a compound interest rate of 4% per annum is $2249.73, obtained by using the compound interest formula with the principal amount of $2000.
Step-by-step explanation:
To calculate the value of Evan's investment after three years with a 4% per annum compound interest rate, we can use the compound interest formula:
A = P(1 + r/n)nt
Where:
- A is the amount of money accumulated after n years, including interest.
- 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 for, in years.
For Evan's investment:
- P = $2000
- r = 4% or 0.04
- n = 1 (compounded annually)
- t = 3 years
Thus, we substitute the values into the formula:
A = 2000(1 + 0.04/1)1\*3
A = 2000(1 + 0.04)3
A = 2000(1.04)3
The calculation will yield the final amount after three years:
A = 2000\*1.124864 = $2249.73
The value of Evan's investment after three years, compounded annually at a 4% rate, will be $2249.73.