What is the present value of $100,000 ten years from now at 6% annual interest?

Conditions

• The future value FV is $100,000.
• The annual interest rate r is 6% (0.06).
• The number of periods n is 10 years.
• Compounding is annual.

Reasoning, step by step

1. Identify the given values: $FV = 100,000$, $r = 0.06$, $n = 10$.
2. Use the present value formula: $PV = \frac{FV}{(1+r)^n}$.
3. Substitute the values: $PV = \frac{100,000}{(1+0.06)^{10}}$.
4. Simplify the denominator base: $1 + 0.06 = 1.06$.
5. Calculate the power: $(1.06)^{10} \approx 1.7908$.
6. Divide the future value by the calculated factor: $100,000 / 1.7908 \approx 55,839.48$.
7. Conclude that $55,839.48 today is equivalent to $100,000 in 10 years at 6% interest.

Example

The video explicitly calculates this: $PV = \frac{100,000}{(1.06)^{10}} = 55,839.48$. The speaker reads the answer as "fifty-five thousand eight hundred thirty-nine dollars and forty-eight cents."

Common misconceptions

• Multiplying by $(1.06)^{10}$ instead of dividing.
• Using simple interest instead of compound interest.
• Incorrectly entering the exponent or base into a calculator.

Watch the explanation

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