Combining Formulas for Accumulated Amount of Money

In summary, we discussed two formulas for calculating the accumulated amount of money: P*e^(rt) for continuous compounding of rate, and F=A(((1+i)^n-1)/i) for annual compounding of rate with frequent savings. It is possible to combine these formulas by using the effective monthly rate from the continuous formula in place of the actual rate in the other formula."
  • #1
Lobotomy
58
0
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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  • #2
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.
 

1. How do I calculate the final accumulated amount of money using multiple formulas?

To calculate the final accumulated amount of money using multiple formulas, you will need to first determine the initial amount of money, the interest rate, and the time period. Then, you can use the appropriate formula for each time period (e.g. annual, monthly, daily) to calculate the interest earned. Finally, add the interest earned to the initial amount to get the final accumulated amount.

2. Can I use different interest rates for each time period when combining formulas?

Yes, you can use different interest rates for each time period when combining formulas. This is known as compound interest, where the interest earned in each time period is added to the initial amount for the next time period. Just make sure to use the correct formula for each time period and use the corresponding interest rate.

3. Is it necessary to have the same time period for each formula when combining them?

No, it is not necessary to have the same time period for each formula when combining them. As long as you use the correct formula for each time period and use the corresponding interest rate, you can have different time periods for each formula. However, it may be easier to use the same time period for all formulas to avoid confusion.

4. Can I use combining formulas for any type of investment?

Yes, you can use combining formulas for any type of investment as long as you have the necessary information such as the initial amount, interest rate, and time period. Combining formulas can be used for simple investments like savings accounts, as well as more complex investments like stocks or real estate.

5. How accurate are the results when combining formulas for accumulated amount of money?

The accuracy of the results when combining formulas for accumulated amount of money depends on the accuracy of the initial information and the formulas used. As long as the information and formulas are correct, the results should be accurate. However, there may be slight variations due to rounding or compounding frequency. It is always a good idea to double check your calculations for accuracy.

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