If you invest $1000 a year at the beginning of each year for the next twenty-five years in a broadly-based stock market fund which historically has earned 7% per year

If you invest $1000 a year at the beginning of each year for the next twenty-five years in a broadly-based stock market fund which historically has earned 7% per year, how much will you expect have at the end of these 25 years if you believe stock market history is an excellent guide to the future PLEASE USE EXCEL TO CALCULATE ?

Solutions

Expert Solution

FV of Annuity Due:
Annuity is series of cash flows that are deposited at regular intervals for specific period of time at the beginning of the each period.

FV of Annuity = (1+r) * CF [ (1+r)^n - 1 ] / r
r - Int rate per period = 7 %
n - No. of period = 25 years

Particulars	Amount
yearly investment	$ 1,000.00
Int Rate	7.000%
Periods	25

FV of Annuity Due = ( 1+ r) [ Cash Flow * [ [ ( 1 + r )^n ] - 1 ] /r ]
= ( 1 + 0.07 ) * [1000 * [ [(1+0.07)^25] - 1 ] / 0.07 ]
= ( 1.07 ) * [1000 * [ [( 1.07 ) ^ 25 ] - 1 ] / 0.07 ]
= ( 1.07 ) * [1000 * [ [ 5.4274 ] - 1 ] / 0.07 ]
= ( 1.07 ) * [ $ 63249.04 ]
= $ 67676.47

Expected amount at the end of 25 years = $ 67676.47

Using EXCEL

FV of Annuity Due:

= FV(rate,nper,pmt,[pv],[type])

rate = 7 % or 0.07

nper = no. of periods = 25

pmt = annual paymnet = $ 1000

PV = This specifies the present value (PV) of the investment/loan . ommitted

Type : for annuity amount type 0 , this means amount deposited at the end of the year

for annuity due amount type 1 , this means amount deposited at the begging of the year

FV of Annuity Due( excel) = FV(7%,25,1000,,1) = $ 67676.47

jeff jeffy answered 1 year ago

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