Question

John has won the mega-bucks lottery, which pays $1, 000, 000. Suppose he deposits the money in a savings account that pays an annual interest of 8% compounded continuously. How long will this money last if he makes annual withdrawals of $100, 000?

Answer 1

Answer:20.91

Explanation:

Given

Principal amount invested=
`\$ 1,000,000`

Rate of interest=8%

Annual Withdrawl=
`\$ 100,000`

compound interest is given by

A=
`\left (1+ (r)/(100)\right )^t`

Therefore reamining Amount after certain years

Net money will become zero after t year

`1,000,000\left (1+ (8)/(100) \right )^t - 100,000\left ( (\left ( 1.08\right )^(t)-1)/(0.08)\right )`=0

`0.8\left ( 1.08\right )^t=\left ( 1.08\right )^(t)-1`

t=20.91 years