Longest Winning Streak in Jeopardy History: An Investment Scenario
Ken Jennings' Investment in an Annuity
As the contestant with the longest winning streak in the history of Jeopardy, Ken Jennings won more than $2.5 million. Suppose he invested $1.6 million in an ordinary annuity that earned 9.6%, compounded monthly. How much would he receive at the end of each month for the next 20 years?
Answer:
Total amount = $10,906,400
He would receive = $45,443.33 every month
Explanation:
Ken invested $1.6 million at 9.6% for 20 years compounded monthly.
n = 20 * 12 = 240
t = 20
P = $1,600,000
R = 9.6% = 0.096
Amount A is equal to
A = P(1+r/n)^(nt)
A = $1,600,000(1+(0.096/240))^(240*20)
A = $1,600,000(1 + (6.857*10^-4))^(2800)
A = $1,600,000(1.0006857)^2800
A = $1,600,000 * 6.8165
A = $10,906,400
Every month, he will get
$10,906,400 / (12 * 20)
= $10,906,400 / 240
= $45,443.33
Answer:
Therefore, he would receive $15,018.74 at the end of each month.
Explanation:
$1.6 million investment is the present value (PV)
PV = $1,600,000
Interest Rate(r) = 9.6% or 0.096 compounded monthly = (0.096÷12) = 0.008
Period(n) = 20 years = (20×12) = 240 months
Ordinary value of annuity:
Annuity = (rate × PV) ÷ (1 - (1 + r)^-240)
Annuity = (0.008 × $1,600,000) ÷ (1 - (1 + 0.008)^-240)
Annuity = ($12,800) ÷ (1 - (1.008)^-240)
Annuity = $12,800 ÷ 0.8522687768
Annuity = $15,018.74
Therefore, he would receive $15,018.74 at the end of each month.
What was the total amount Ken Jennings would receive at the end of each month if he invested $1.6 million in an ordinary annuity with a 9.6% interest rate compounded monthly for 20 years? Ken Jennings would receive $10,906,400 in total and $45,443.33 at the end of each month.