Final answer:
To find the initial investment required to provide an annuity of $10,000 per year for the next 20 years with a discount rate of 8%, you can use the formula for the present value of an annuity.
Step-by-step explanation:
To find the initial investment required to provide an annuity of $10,000 per year for the next 20 years with a discount rate of 8%, we can use the formula for the present value of an annuity. The formula is:
PV = C * ((1 - (1+r)^-n) / r)
Where PV is the present value, C is the cash flow per period, r is the discount rate, and n is the number of periods. Plugging in the values, we have:
PV = $10,000 * ((1 - (1+0.08)^-20) / 0.08)
Simplifying the expression, we get:
PV = $10,000 * (13.5910295 / 0.08) = $169,376.61
Therefore, the initial investment required is $169,376.61.