SOLUTION: Many young people do not start saving right away for retirement, although by the time that they do, they may be earning more and thus be able to afford to save more each month.

Question 71954: Many young people do not start saving right away for retirement, although by the time that they do, they may be earning more and thus be able to afford to save more each month.
a) How much will be in your fund if at age 65 if you dont start saving until age 35 and at that age start saving 100 per month in account paying a steady 6% annual interest compounded monthly?
b) Suppose instead that you have children young, pay for their colege expenses, and finally start saving for retirement at age 45. How much do you have to save per month, with a steady return of 7.5% compunded monthly, to accumulate
$ 250,000.00 by age 65?
Answer by stanbon(57361) (Show Source):
You can put this solution on YOUR website!
a) How much will be in your fund if at age 65 if you dont start saving until age 35 and at that age start saving 100 per month in account paying a steady 6% annual interest compounded monthly?
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This is called "future value of an ordinary annuity".
Formula:
S = R[(1+i)^n - 1]/i
S is the future value
R is the periodic deposit
i is the interest for that period
n is the number of periods
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In you case:
S = ?
R = 100
i = (0.06)/12 = 0.005
n=30 yrs *12 = 360 periods between age 35 and 65
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S = 100[(1.005)^360 - 1]/0.005
S=$100,451.50
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b) Suppose instead that you have children young, pay for their colege expenses, and finally start saving for retirement at age 45. How much do you have to save per month, with a steady return of 7.5% compunded monthly, to accumulate
$ 250,000.00 by age 65?
250,000 = R[(1+(0.075/12)^(20*12)]/(0.075/12)
1562.5= R[(1.00625)^(240) - 1]
1562.5 = R[3.460817031...]
R = $451.48 per month
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Cheers,
Stan H.