Question

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.

Answer 1

see the explanation

Explanation:

we know that

step 1

The compound interest formula is equal to

`A=P(1+(r)/(n))^(nt)`

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

`r=10\%=10/100=0.10\\n=4`

substitute in the formula above

`A=P(1+(0.10)/(4))^(4t)`

`A=P(1.025)^(4t)`

Applying property of exponents

`A=P[(1.025)^(4)]^(t)`

`A=P(1.1038)^(t)`

step 2

The formula to calculate continuously compounded interest is equal to

`A=P(e)^(rt)`

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

`r=10\%=10/100=0.10`

substitute in the formula above

`A=P(e)^(0.10t)`

Applying property of exponents

`A=P[(e)^(0.10)]^(t)`

`A=P(1.1052)^(t)`

step 3

Compare the final amount

`P(1.1052)^(t) > P(1.1038)^(t)`

therefore

Find the difference

`P(1.1052)^(t) - P(1.1038)^(t)` ----> 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.