Final answer:
Using the future value of an annuity formula, a $3,000 annual contribution to a retirement account earning 6% interest will be worth approximately $96,700 in 20 years, which rounds off to $96,780, so Option B) $96,780 is the correct answer.
Step-by-step explanation:
To calculate the future value of a series of annual contributions to a retirement account, we use the future value of an annuity formula. This type of calculation involves compound interest, which is the interest on both the initial principal and the accumulated interest of previous periods of a deposit or loan.
The question asks what a $3,000 annual contribution to a retirement account earning 6% will be worth in 20 years. We can apply the formula for the future value of an annuity to find this:
Future Value = Pmt × {[{(1 + r)^{n} -1}] / r}
Where:
- Pmt is the annual payment ($3,000)
- r is the interest rate per period (0.06)
- n is the total number of payments (20)
Plugging in the numbers:
Future Value = $3,000 × {[{(1 + 0.06)^{20} - 1}] / 0.06}
Future Value ≈ $96,700 (rounded to the nearest tens)
Therefore, the correct answer is that a $3,000 annual contribution after 20 years is option B) $96,780.