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https://www.thecalculatorsite.com/finance/calculators/compoundinterestcalculator.php
I'd do it with Excel because that's how I do most things.
If it's the former then this would help:
Compound Interest Calculator - Daily, Monthly, Yearly Compounding (thecalculatorsite.com)
X*1.04^n+ X*1.04^n-1 + ... + X*1.04 is equal to X*(1.04^n+ 1.04^n-1 + ... + 1.04), and the stuff inside the brackets is a geometric series, for which there is a formula:
If you multiply the bracket stuff by 1.04 then every exponent increases by 1, so if you multiply the bracket stuff by 1.04 - 1, then you get 1.04^(n+1) - 1.04 and all the intermediate powers cancel out.
In other words, 1.04^n+ 1.04^n-1 + ... + 1.04 is equal to (1.04^(n+1) - 1.04) / (1.04-1). And you can even calculate 1.04 - 1 = 0.04, to simplify it further. So your original total becomes
X*(1.04^(n+1) - 1.04) / 0.04.
Yes, the scenario you're describing is a common one in finance, often related to calculating the future value of a series of equal, annual deposits or investments, known as an annuity. The formula you're looking for is for the future value of an annuity compounded annually. The general formula to calculate the future value of such an annuity is:
FV=P×((1+r)n−1r)FV=P×(r(1+r)n−1)
Where:
FVFV is the future value of the annuity.
PP is the annual payment (the amount you deposit every year).
rr is the annual interest rate (expressed as a decimal).
nn is the number of years the money is deposited or invested for.
In your case:
P=1000P=1000
r=0.04r=0.04 (4% annual interest rate)
n=5n=5 years
Plugging these values into the formula gives:
FV=1000×((1+0.04)5−10.04)FV=1000×(0.04(1+0.04)5−1)
FV=1000×(1.2166529−10.04)FV=1000×(0.041.2166529−1)
FV=1000×(0.21665290.04)FV=1000×(0.040.2166529)
FV=1000×54.163225FV=1000×54.163225
FV=5416.3225FV=5416.3225
Therefore, after 5 years, the future value of your annuity, with a $1000 annual deposit at an annual interest rate of 4%, would be approximately $5416.32. This formula simplifies the calculation by summing the compounded value of each annual deposit into a single equation, rather than calculating each year's compound interest individually and summing them.
https://www.thefretboard.co.uk/discussion/202071/nco