Question

You have 25 years left until retirement and want to retire with $1.1 million. Your salary is paid annually, and you will receive $61,000 at the end of the current year. Your salary will increase at 4 percent per year, and you can earn a return of 10 percent on the money you invest. If you save a constant percentage of your salary, what percentage of your salary must you save each year?

Answer 1

percentage of your salary save each year is 13.24%

Step-by-step explanation:

given data

time period t = 25 year

amount = $1.1 million

salary = $61000

increase r1 = 4 percent per year = 0.04

return r2 = 10 percent = 0.1

to find out

what percentage of your salary must you save each year

solution

we consider here annual saving = A

so amount formula is

amount = A ×
`((1+r1)^t -(1+r2)^t)/(r1-r2)`

here A is annual saving and r1 is increase rate and r2 is return rate

1100000 = A ×
`(1.1^(25) - 1.04^(25))/(0.1-0.04)`

A = $8079.45

so

proportion of salary is
`(8079.45)/(61000)`

proportion of salary = 13.24%

so percentage of your salary save each year is 13.24%