Bianca deposited $1500 into asavings account for whichsimple interest is calculatedquarterly. If her $1500 grew to$1509 after 3
months, what isthe yearly interest rate onBianca's account?
1 answer:
Solution:
Given;
![P=1500,A=1509,t=3months=0.25year](https://tex.z-dn.net/?f=P%3D1500%2CA%3D1509%2Ct%3D3months%3D0.25year)
![\begin{gathered} A=P(1+\frac{r}{4})^{4t} \\ \\ 1509=1500(1+\frac{r}{4})^{4(0.25)} \\ \\ \frac{1509}{1500}=1+\frac{r}{4} \\ \\ 1.006-1=\frac{r}{4} \\ \\ r=4(0.006) \\ \\ r=0.024 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A%3DP%281%2B%5Cfrac%7Br%7D%7B4%7D%29%5E%7B4t%7D%20%5C%5C%20%20%5C%5C%201509%3D1500%281%2B%5Cfrac%7Br%7D%7B4%7D%29%5E%7B4%280.25%29%7D%20%5C%5C%20%20%5C%5C%20%5Cfrac%7B1509%7D%7B1500%7D%3D1%2B%5Cfrac%7Br%7D%7B4%7D%20%5C%5C%20%20%5C%5C%201.006-1%3D%5Cfrac%7Br%7D%7B4%7D%20%5C%5C%20%20%5C%5C%20r%3D4%280.006%29%20%5C%5C%20%20%5C%5C%20r%3D0.024%20%5Cend%7Bgathered%7D)
Thus, the yearly interest rate on Bianca's account is 2.4%
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