Combining Formulas for Accumulated Amount of Money

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SUMMARY

The discussion focuses on combining two financial formulas to calculate the accumulated amount of money with continuous compounding and frequent deposits. The first formula, P*e^(rt), is used for continuous compounding, while the second formula, F=A(((1+i)^n-1)/i), applies to regular deposits with annual compounding. The key insight is that one can derive an effective monthly rate from the continuous compounding formula and substitute it into the second formula to account for multiple deposits per year.

PREREQUISITES
  • Understanding of continuous compounding in finance
  • Familiarity with the formula P*e^(rt)
  • Knowledge of the formula F=A(((1+i)^n-1)/i)
  • Basic concepts of effective interest rates
NEXT STEPS
  • Research how to derive effective interest rates from continuous compounding
  • Learn about the implications of frequent deposits on accumulated wealth
  • Explore financial calculators that handle both continuous and discrete compounding
  • Investigate the differences between annual and monthly compounding methods
USEFUL FOR

Finance students, investment analysts, and anyone involved in personal finance who seeks to optimize savings strategies through effective compounding techniques.

Lobotomy
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Hi
P*e^(rt) = Accumulated amount of money

Principal
e logaritm
rate
time

is for continuous compounding of rate.


F=A(((1+i)^n-1)/i)
and this one works for savings that are made frequently like every month or so but only with annual compounding of rate.

is there any way to combine these formulas and calculate the accumulated amount of money i.e. getting a formula that express continuous compounding of rate for when you deposit money X times per year.
 
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You can find the effective monthly rate with the contimnuous formula, then use that effective rate instead of the actual rate in the other formula.
 

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