: How to calculate the compound interest for the following scenario Mr A plans to invest 100000 every year for 15 years (he will withdraw money at the end of 15 years) and is expecting a return of about 12%. I know the FV

The future value is found by summing compounded deposits

fv = ?(1 + r)^k for k = 1 to n

? by induction the future value formula is

fv = (d (1 + r) (-1 + (1 + r)^n))/r

Using the OP's figures

d = 100000
r = 0.12
n = 15

fv = (d (1 + r) (-1 + (1 + r)^n))/r = 4175328.04

In Excel

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

type - [optional] When payments are due. 0 = end of period, 1 = beginning of period. Default is 0.

Savings deposits are usually made at the beginning of the period.

=FV(0.12, 15, 100000, 0, 1)

In the unlikely case that Mr A plans to invest at the end of each year, in which case he would withdraw money at the same time as making the last deposit, use

=FV(0.12, 15, 100000)

Equivalent to

fv = ?(1 + r)^(k - 1) for k = 1 to n

? fv = (d (-1 + (1 + r)^n))/r = 3727971.47

The summation can also be written in Excel like so

=SERIESSUM(1+0.12,0,1,{100000,100000,100000,100000,100000,100000,100000,100000,
100000,100000,100000,100000,100000,100000,100000})

It looks like the following should also work but it doesn't.

=SERIESSUM(1+0.12,0,1,TRANSPOSE(ROW(INDIRECT("1:15")))^0*100000)

If anyone can suggest why that would be interesting.

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