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Sagot :
Given:
a statement is given about the simple interest and compound interest as following
"You deposit $450 into an account that earns simple interest at a rate of 8% APR. Your cousin deposits $450 into an account that has the same interest rate, but the interest is compounded annually"
Find:
we have to answer part (a) and part(b) as asked in the question.
Explanation:
part(a):
Principal (P) = $450
interest rate R = 8%
Time(t) = 5 years
Therefore, Simple interest is
[tex]S.I.=\frac{P\times R\times t}{100}=\frac{450\times8\times5}{100}=180[/tex]Therefore amount after 5 year = Principal + Simple interest
= $450 + $180
= $630
Ending Balance = $630
part(b):
Principal (P) = $450
interest rate R = 8% (Compounded annually)
interest in decimal r = 8/100 = 0.08 rate per year
Time(t) = 5 years
Amount after 5 year is
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=450(1+\frac{0.08}{1})^{(1)(5)} \\ A=661.20 \end{gathered}[/tex]Therefore, total amount after 5 year is $661.20.
Ending Balance = $661.20
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