Final answer:
To calculate how much you would have after investing $9,800 annually for 7 years at 9%, you use the future value of an annuity formula. Plug in the payment per period, interest rate, and number of periods into the formula or a financial calculator to compute the final amount.
Step-by-step explanation:
To determine how much you would have after investing $9,800 per period for 7 years at a 9% interest rate, we would use the future value of an annuity formula. The formula for the future value of an annuity is FV = P * [((1 + r)^n - 1) / r], where P is the payment per period, r is the interest rate per period, and n is the number of periods.
Using the formula and a financial calculator, you would input the following values:
- P (the payment per period): $9,800
- r (the interest rate per period): 9% or 0.09
- n (the number of periods): 7 (years)
This results in FV = $9,800 * [((1 + 0.09)^7 - 1) / 0.09]. Calculating this will give you the total amount after 7 years.
Remember that compound interest significantly increases the future value of your investments over time. Starting to save money early, as the example with $3,000 invested at a 7% return over 40 years shows, can result in substantial growth due to compound interest.