The final value of compound interest with the fractional interest

The length of the flaring process of a capital is not just an integer.

Formula of Final Value of Compound Interest With Fractional interest

C_n = C(1 + i)^m (1 + p.i)

Information :
Cn = Capital in period n
C = Initial capital period
p = Fractional period
i = Percentage of interest
m = Value of grappler from fractional period

Example of the Final Value of Compound Interest with the Fractional interest

Capital of $4,500,000 is levied with 3%/month compound interest rate. Please determine the final capital after flowering for 5.75 months!

Answer:
C = $ 4,500,000
i = 3% / month = 0.03 / month
n = 5.75 months
m = 5 months
p = 5.75 - 5 = 0.75

C_n = C(1 + i)^m (1 + p.i)
C_5.75 = 4,500,000(1 + 0.03)⁵ (1 + (0.75).(0.03))
C_5.75 = 4,500,000(1.03)⁵ (1.0225)
C_5.75 = 5,334,109.83

So the final capital after flowering for 5.75 months is $5,334,109.83.

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