Respuesta :
The amount of money more in the account of Charlotte after 19 years than the money in account of Alyssa is, $13035.13
How to calculate the compound interest?
Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.
The formula for the final amount with the compound interest formula can be given as,
[tex]A=P\times\left(1+\dfrac{r}{n\times100}\right)^{nt}\\[/tex]
Here, A is the final amount (principal plus interest amount) on the principal amount P of with the rate r of in the time period of t.
Charlotte invested $33,000 in an account paying an interest rate of 7 3/4% compounded continuously for 19 years. The rate of interest is,
[tex]r=7\dfrac{3}{4}\\r=\dfrac{31}{4}\\r=7.75[/tex]
Thus, the final amount in his account after 19 years is,
[tex]A=33000\times\left(1+\dfrac{7.75}{360\times100}\right)^{360(19)}\\A=143861.22[/tex]
Alyssa invested $33,000 in an account paying an interest rate of 7 1/4% compounded daily. The rate of interest is,
[tex]r=7\dfrac{1}{4}\\r=\dfrac{29}{4}\\r=7.25[/tex]
Thus, the final amount in her account after 19 years is,
[tex]A=33000\times\left(1+\dfrac{7.75}{360\times100}\right)^{360(19)}\\A=130826.09[/tex]
The more money would Charlotte have in her account than Alyssa is,
[tex]D=143861.22-130826.09\\D=13035.13[/tex]
Thus, the amount of money more in the account of Charlotte after 19 years than the money in account of Alyssa is, $13035.13
Learn more about the compound interest here;
https://brainly.com/question/24274034
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