The amount of interest Molly will earn after 5 years on a deposit of [tex]\$100[/tex] compounded annually over 5 years is [tex]\$27.63[/tex]
First, we need to find the future value of her investment, then we subtract the original deposit from it to get the amount of interest she will get at the end of 5 years.
The future value of an investment that is compounded annually is given by
[tex]A=P(1+r)^t[/tex]
where
[tex]A=\text{Amount of money in Molly's account after 5 years}\\P=\text{Molly's initial deposit into her account}=\$500\\r=\text{The annual interest rate as a decimal}=0.05\\t=\text{The time the money is invested (in years)}=5[/tex]
Substituting the available values into the formula and solving
[tex]A=100(1+0.05)^5=100(1.05)^5 \approx \$ 127.63[/tex]
The interest Molly will earn after 5 years is
[tex]A-P=\$127.63-\$100=\$27.63[/tex]
Therefore, the amount of interest Molly will earn after 5 years on a deposit of [tex]\$100[/tex] compounded annually over 5 years is [tex]\$27.63[/tex]
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