Final answer:
The future value of a $1000 investment with 4% interest compounded monthly will be $1123.60, while with yearly compounding it will be $1124.86. Therefore, the better investment option is to compound the interest yearly for a higher future value.
So, the correct answer is B.
Step-by-step explanation:
To calculate the future value of an investment with compound interest, we can use the formula:
A = P (1+r/n)^(nt)
Where:
- A is the future value of the investment
- P is the principal amount (the initial investment)
- r is the annual interest rate (written as a decimal)
- n is the number of times interest is compounded per year
- t is the number of years
In this case, we have:
- P = $1000
- r = 4% = 0.04
- n = 12 (compounded monthly)
- t = 3
Using this information, we can calculate the future value of the investment with monthly compound interest:
A = 1000(1+0.04/12)^(12*3) = $1123.60
Next, we can calculate the future value of the investment with yearly compound interest:
A = 1000(1+0.04)^3 = $1124.86
Comparing these values, we can see that the investment with monthly compound interest ($1123.60) is lower than the investment with yearly compound interest ($1124.86).
Therefore, the better investment option is to compound the interest yearly because it results in a higher future value ($1124.86).
So, the correct answer is B.