Victor Vogel is 27 years old and currently earns $65,000 per year. He recently picked a winning number in the Wisconsin lottery. After income taxes he took home $1,000,000. Victor put the entire amount into an account earning 5% per year, compounded annually. He wants to quit his job, maintain his current lifestyle and withdraw enough at the beginning of each year to replace his salary. At this rate, how long will the winnings last?

27.03   years

Step-by-step explanation:

The nper excel function can be used to determine the period in which the winnings would last as below:

=nper(rate,pmt,-pv,fv,type)

rate is the annual interest rate on the account

pmt is the amount of annual withdrawal which is $65000

pv is the current amount in the account which is $1,000,000

fv is the future balance in the account after all withdrawals are made i.e$0

type is 1 which  means withdrawals are made at the beginning of the year

=nper(5%,65000,-1000000,0,1)= 27.03  

+25 = x

step-by-step explanation:

here x is the hypotenuse of a right triangle whose legs are 7 and 24.   by the pythagorean theorem, 7² + 24² must equal x²:

x² = 49 + 576 = 625.   thus, x = +√625 = +25 = x