Using continuous compounding and compound interest, it is found that Matthew would have $17 more than Elizabeth in his account.
Compound interest:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
Continuous compounding:
[tex]A(t) = Pe^{rt}[/tex]
The parameters are:
For both of them:
Elizabeth:
Then:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(8) = 970\left(1 + \frac{0.06625}{365}\right)^{365(8)}[/tex]
[tex]A(8) = 1648[/tex]
Matthew:
Then:
[tex]A(t) = Pe^{rt}[/tex]
[tex]A(8) = 970e^{0.0675(8)}[/tex]
[tex]A(8) = 1665[/tex]
The difference is:
1665 - 1648 = 17
Hence, Matthew would have $17 more than Elizabeth in his account.
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