Final answer:
To find out the monthly annuity payments that Ken Jennings will receive, the present value of an annuity formula would be used, accounting for the interest rate per period and the total number of periods. Given the 4.25% annual interest rate, compounded monthly over 20 years, financial calculator or software would determine the monthly payment from a $1.2 million investment.
Step-by-step explanation:
To calculate the monthly payments for an ordinary annuity, we need to use the formula for the present value of an annuity. The formula takes into account the regular payments (R), the interest rate per period (i), and the number of periods (n):
PV = R x ((1 - (1 + i)^-n) / i)
In this case, Ken Jennings invested $1.2 million at a 4.25% annual interest rate, compounded monthly, to be distributed over 20 years. First, we convert the annual interest rate to a monthly rate by dividing by 12 (the number of months in a year), which gives us a monthly interest rate of 0.3541667%. Next, we calculate the number of periods, which is 20 years times 12 months per year, equaling 240 periods.
Upon substituting the applicable values into the formula and solving for R, we can determine the monthly amount Ken Jennings would receive.
It's important to note that this requires the use of a financial calculator or software capable of performing such calculations, as it involves finding the value of a variable in an annuity present value formula, which is not a straightforward algebraic manipulation.
Moreover, the power of compound interest plays a significant role in investments over time, as seen in the provided examples. It substantially increases the value of the investment, demonstrating the benefits of starting to save and invest early in life.