Determine the term of a 39000 investment with an interest rate of 2.06% compounded quarterly, if the future value is 52000 Select one: a. 16 years b. 17 years c. 15 years d. 14 years

## Step 1: Convert the interest rate to a decimal and per quarter.### The given annual interest rate is . Convert this to a decimal by dividing by 100, resulting in . Since the interest is compounded quarterly, divide the annual rate by 4 to find the quarterly rate: .## Step 2: Set up the compound interest formula.### The formula for compound interest is , where is the future value, is the principal, is the annual interest rate, is the number of times interest is compounded per year, and is the time in years. In this case, 52000 P = \ , , and . We want to solve for . The formula becomes .## Step 3: Simplify and solve for .### Simplify the equation: , which becomes . Divide both sides by 39000: , which simplifies to . Take the natural logarithm of both sides: . Use the logarithm power rule: . Solve for : . Calculate the value of : .