Investment in a mutual fund, how much is the return?

flora33

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Mar 10, 2008
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Your sister turned 30 today, and she is planning to save $3,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund, which she expects to provide a return of 10% per year. She plans to retire 35 years from today, when she turns 65, and she expects to live for 30 years after retirement, to age 95. Under these assumptions, how much can she spend in each year after she retires? Her first withdrawal will be made at the end of her first retirement year.


a) $78,976
b) $91,110
c) $88,513
d) $86,250
e) $83,049

The way I worked this one out was to find the FV using a compound interest calculator. I am getting $897,380.42 at the end of 35 years investing. If you divide this over 30 years the total is $29912.68. This is obviously way off any of the possible answers. I am missing a step. Any hints? It is much appreciated!

Flora
 
Your sister turned 30 today, and she is planning to save $3,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund, which she expects to provide a return of 10% per year. She plans to retire 35 years from today, when she turns 65, and she expects to live for 30 years after retirement, to age 95. Under these assumptions, how much can she spend in each year after she retires? Her first withdrawal will be made at the end of her first retirement year.

The accumulated amount at the end of the 35 years derives from

S = R[(1+i)^n - 1]/i where
S = the accumulated sum
R = the annual deposit
i = the decimal interest rate per year
n = the number of deposits

This yields an accumulation of $813,073.10.

The annual payout of this annuity derives from

R = Pi/[1 - (1+i)^(-n)] yielding (d) as the correct answer.

a) $78,976
b) $91,110
c) $88,513
d) $86,250
e) $83,049

The way I worked this one out was to find the FV using a compound interest calculator. I am getting $897,380.42 at the end of 35 years investing. If you divide this over 30 years the total is $29912.68. This is obviously way off any of the possible answers. I am missing a step. Any hints? It is much appreciated!
 
TchrWill said:
Your sister turned 30 today, and she is planning to save $3,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund, which she expects to provide a return of 10% per year. She plans to retire 35 years from today, when she turns 65, and she expects to live for 30 years after retirement, to age 95. Under these assumptions, how much can she spend in each year after she retires? Her first withdrawal will be made at the end of her first retirement year.

The accumulated amount at the end of the 35 years derives from

S = R[(1+i)^n - 1]/i where
S = the accumulated sum
R = the annual deposit
i = the decimal interest rate per year
n = the number of deposits

This yields an accumulation of $813,073.10.

The annual payout of this annuity derives from

R = Pi/[1 - (1+i)^(-n)] yielding (d) as the correct answer.

a) $78,976
b) $91,110
c) $88,513
d) $86,250
e) $83,049

The way I worked this one out was to find the FV using a compound interest calculator. I am getting $897,380.42 at the end of 35 years investing. If you divide this over 30 years the total is $29912.68. This is obviously way off any of the possible answers. I am missing a step. Any hints? It is much appreciated!

Thanks a lot for you help on both of these questions! I really appreciate it!

Flora
 
Code:
Year               Deposit       Interest           Balance
  1                3000.00           .00             3000.00
  2                3000.00        300.00             6300.00  : 3000 * .10 = 300
  3                3000.00        630.00             9930.00  : 6300 * .10 = 630
  4                3000.00        993.00            13923.00  : 9930 * .10 = 993
  5                3000.00       1392.30            18515.30  :13923 * .10 = 1392.30
If you can "picture" what's happening when $3000 is deposited annually
and earns 10% interest (like shown above), then things will be easier for you.

The "formula" for calculating above is A[(1 + i)^n - 1] / i
A = amount of annual deposit
n = number of years
i = interest rate (10% = .10)

3000[(1 + .10)^5 - 1] / .10 = 18515.30

Once you "get the hang" of these, you'll find 'em easy nuff....
 
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