Final answer:
To find the future value of an investment compounded annually, use the formula FV = Principal × (1 + interest rate)^time. With a principal of $125,000, a 3.4% interest rate, and over 3 years, the future value equals $138,181.87, and the compound interest earned is $13,181.87.
Step-by-step explanation:
The future value of an investment when interest is compounded is found using the formula:
FV = Principal × (1 + interest rate)^time
In this case, the principal (P) is $125,000, the annual interest rate (r) is 3.4% (or 0.034 in decimal form), and the time (t) is 3 years.
To find the future value for annual compounding, we would calculate it as follows:
FV = $125,000 × (1 + 0.034)^3
First, add 1 to the interest rate: 1 + 0.034 = 1.034.
Next, raise this sum to the power of the time, which is 3 years: (1.034)^3.
Then multiply the principal by the result to get the future value:
FV = $125,000 × 1.034^3 = $125,000 × 1.105454976 = $138,181.87
The compound interest is then calculated as the difference between this future value and the principal:
Compound interest = Future Value - Principal = $138,181.87 - $125,000 = $13,181.87.