Question

1. You are saving for retirement. You have decided that one year from today you will begin investing 10 percent of your annual salary in a mutual fund which is expected to earn a return of 12 percent per year (compounded semi-annually). Your present salary is $30,000, and you expect that it will grow by 4 percent per year throughout your career (consequently, your investment at time 1 will be $3,000, your investment at time 2 will be $3,120, etc.). You will retire 40 years from today.

a) How much money will you have in your investment account at retirement (assume you make your last investment deposit 40 years from now on the day you retire)?

Please use financial calculator

Answer 1

Answer:

Given

Present salary =$30000

Investment at time 1 P=10%*30000=$3000

Since we are investing a fixed percentage of money into mutual fund so growth rate of investment in mutual fund will be same as growth rate of salary.

Growth rate in investment in mutual fund G =Growth rate of salary =4%

Nominal Annual Return R= 12% compounded semi annually.

So effective annual rate r=(1+R/2)^2-1=(1+12%/2)^2-1=12.36%

N=40 years

So Amount at retirement will be A= P*{(1+r)^N-(1+G)^N}/(r-G)=3000*((1+12.36%)^40-(1+4%)^40)/(12.36%-4%)

A=$3624221.514