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.