Answer:
see the explanation
Step-by-step explanation:
we know that
step 1
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
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
[tex]r=10\%=10/100=0.10\\n=4[/tex]
substitute in the formula above
[tex]A=P(1+\frac{0.10}{4})^{4t}[/tex]
[tex]A=P(1.025)^{4t}[/tex]
Applying property of exponents
[tex]A=P[(1.025)^{4}]^{t}[/tex]
[tex]A=P(1.1038)^{t}[/tex]
step 2
The formula to calculate continuously compounded interest is equal to
[tex]A=P(e)^{rt}[/tex]
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
[tex]r=10\%=10/100=0.10[/tex]
substitute in the formula above
[tex]A=P(e)^{0.10t}[/tex]
Applying property of exponents
[tex]A=P[(e)^{0.10}]^{t}[/tex]
[tex]A=P(1.1052)^{t}[/tex]
step 3
Compare the final amount
[tex]P(1.1052)^{t} > P(1.1038)^{t}[/tex]
therefore
Find the difference
[tex]P(1.1052)^{t} - P(1.1038)^{t}[/tex] ----> 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.
