Question

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 1

Answer:

Total amount = $10906400

He would receive = $ 45443.33 every month

Explanation:

Ken invested $1.6 million at 9.6% for 20 yes compounded monthly.

n = 20*12= 140

t = 20

P= 1600000

R= 9.6% = 0.096

Amount A is equal to

A = p(1+r/n)^(nt)

A =

1600000(1+(0.096/140))^ (140*20)

A =

1600000(1 + (6.857*10^-4))^(2800)

A= 1600000(1.0006857)^2800

A = 1600000*6.8165

A = 10906400

Every month, he will get

10906400/(12*20)

= 10906400/240

=$ 45443.333

Answer 2

Answer: Therefore, he would recieve $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 recieve $15,018.74 at the end of each month.