Find the future value of an investment of $10 ,500 if it is invested for six years and compounded semiannually at an annual rate of 3%. Use the $1.00 future value table or the future value and compound interest formula.
i = .03/2 = .015
n = 6(2) = 12
amount = 10500(1.015)^12
= ...
12 553.9908
To find the future value of an investment, we can use the formula for compound interest:
Future Value = Principal * (1 + interest rate / n)^(n * time)
Where:
- Principal is the initial investment amount ($10,500 in this case)
- Interest rate is the annual interest rate (3% in this case)
- Time is the number of years the investment is held for (6 years in this case)
- n is the number of compounding periods per year (semiannually, so n = 2)
Let's calculate the future value step by step:
Step 1: Calculate the interest rate per compounding period:
Interest rate per period = Annual interest rate / Number of compounding periods per year
= 3% / 2
= 0.03 / 2
= 0.015
Step 2: Calculate the number of compounding periods:
Number of compounding periods = Number of years * Number of compounding periods per year
= 6 * 2
= 12
Step 3: Calculate the future value using the compound interest formula:
Future Value = $10,500 * (1 + 0.015)^(12)
= $10,500 * 1.015^(12)
≈ $10,500 * 1.19679
≈ $12,562.39
So, the future value of the investment after 6 years will be approximately $12,562.39.