If Nancy invests $10,000 annually at an 8% interest rate for five years, what will the total be worth?

If Nancy invests $10,000 annually at an 8% interest rate for five years, what will the total be worth?

• A. $55,555
• B. $60,000
• C. $63,359
• D. $70,000

Answer: (C)

To determine the future value of Nancy's investment, we can use the future value of an annuity formula, as she is making regular annual contributions. The formula is: FV = P * [(1 + r)^n - 1] / r Where: - FV is the future value of the annuity - P is the annual investment amount - r is the annual interest rate (expressed as a decimal) - n is the number of years In this case: - P = $10,000 - r = 8% = 0.08 - n = 5 years Now plugging these values into the formula: FV = 10,000 * [(1 + 0.08)^5 - 1] / 0.08 Calculating inside the brackets first: (1 + 0.08)^5 = (1.08)^5 ≈ 1.4693 Now, subtracting 1: 1.4693 - 1 ≈ 0.4693 Now, dividing by the interest rate: 0.4693 / 0.08 ≈ 5.8663 Multiplying by the annual investment: FV = 10,000

To determine the future value of Nancy's investment, we can use the future value of an annuity formula, as she is making regular annual contributions. The formula is:

FV = P * [(1 + r)^n - 1] / r

Where:

• FV is the future value of the annuity

• P is the annual investment amount

• r is the annual interest rate (expressed as a decimal)

• n is the number of years

In this case:

• P = $10,000

• r = 8% = 0.08

• n = 5 years

Now plugging these values into the formula:

FV = 10,000 * [(1 + 0.08)^5 - 1] / 0.08

Calculating inside the brackets first:

(1 + 0.08)^5 = (1.08)^5 ≈ 1.4693

Now, subtracting 1:

1.4693 - 1 ≈ 0.4693

Now, dividing by the interest rate:

0.4693 / 0.08 ≈ 5.8663

Multiplying by the annual investment:

FV = 10,000