You find an interest rate of 10% compounded quarterly. Calculate how much more money you would have in your pocket if you had used an account compounded continuously with the same interest rate and principal. Round to the nearest cent and do not include the dollar sign.

NOTE: I only need the formula for this.

see the explanation

Step-by-step explanation:

we know that    

step 1

The compound interest formula is equal to  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

substitute in the formula above

Applying property of exponents

step 2

The formula to calculate continuously compounded interest is equal to

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

substitute in the formula above

Applying property of exponents

step 3

Compare the final amount

therefore

Find the difference

----> Additional amount of money you would have in your pocket if you had used a continuously compounded account with the same interest rate and the same principal.

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