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Hunter invested $750 in an account paying an interest rate of 6\tfrac{5}{8}6 8 5 ​ % compounded continuously. London invested $750 in an account paying an interest rate of 6\tfrac{1}{2}6 2 1 ​ % compounded daily. After 18 years, how much more money would Hunter have in his account than London, to the nearest dollar?

Sagot :

JeanaShupp

Answer: $ 55

Step-by-step explanation:

When interest is compounded continuously, the final amount will be

[tex]A=Pe^{rt}[/tex]

When interest is compounded daily, the final amount will be

[tex]A=P(1+\dfrac{r}{365})^{365t}[/tex]

, where P= Principal , r = rate of interest , t = time

For Hunter , P= $750, r = [tex]6\dfrac{5}{8}\%=\dfrac{53}{8}\%=\dfrac{53}{800}=0.06625[/tex]

t = 18 years

[tex]A=750e^{0.06625(18)}=\$2471.48[/tex]

For London , P= $750, r = [tex]6\dfrac{1}{2}\%=\dfrac{13}{2}\%=\neq \dfrac{13}{200}=0.065[/tex]

t = 18 years

[tex]A=750(1+\dfrac{0.065}{365})^{18(365)}=\$2416.24[/tex]

Difference = $ 2471.48 - $ 2416.24 =$ 55.24≈$ 55

Hence, Hunter would have $ 55 more than London in his account .

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