Expert: Sherry Wallin - 2/7/2009

Question
$5,000 is contributed each year for 40 years and makes an annual return of 8% on the investment.  

Calculate amount of money saved.

Thanks for your assistance.

Answer
Hi Randy~
    Are you asking me to give you a formula to find this or how do you figure out the formula to answer something like this? Based on the way the question is worded it sounds as if it is compounded yearly. So at the end of year 1 you would have 5000+.08(5000)=5400 or 5000(1.08)
end of year 2 you would have another 5000(1.08)+1.08[(5000)(1.08)]
= 5000(1.08) + 5000(1.08)^2 = 5000[(1.08) +(1.08)^2]; end of year 3:
5000(1.08)+ (1.08)5000[(1.08) +(1.08)^2]
= 5000(1.08)+5000[(1.08)^2+(1.08)^3]
= 5000[(1.08)+(1.08)^2+(1.08)^3]
...
end of 40 years:
5000[(1.08)+(1.08)^2+(1.08)^3 + (1.08)^4+...+(1.08)^40]

formula created:
P[(1+r)+(1+r)^2+(1+r)^3+...+(1+r)^n]

in summation notation:
P(sum from k=1 to n)[(1+r)^k]

I'm not sure what level of math you are in but some or all of this should make sense :)

Math Prof