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

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