![A=P(1+ \dfrac{r}{m})^{mt}](https://tex.z-dn.net/?f=%20A%3DP%281%2B%20%5Cdfrac%7Br%7D%7Bm%7D%29%5E%7Bmt%7D%20)
This was the formula that was given.
A is the final amount, which is what we're solving for.
P is the original money amount, which is $5,000
r is the interest rate, which is 1%, or 0.01
m is the amount of times the interest is compounded per year. Since the interest is compounded quarterly, interested is compounded 4 times per year.
t is the time the money is in the bank, which is 2 years
That's all we need to solve the equation now
![A=P(1+ \dfrac{r}{m})^{mt}](https://tex.z-dn.net/?f=%20A%3DP%281%2B%20%5Cdfrac%7Br%7D%7Bm%7D%29%5E%7Bmt%7D%20)
![=5000(1+ \dfrac{0.01}{4})^{4(2)}](https://tex.z-dn.net/?f=%3D5000%281%2B%20%5Cdfrac%7B0.01%7D%7B4%7D%29%5E%7B4%282%29%7D%20)
![=5000(1.0025)^{8}](https://tex.z-dn.net/?f=%20%3D5000%281.0025%29%5E%7B8%7D%20)
![\approx 5100.88](https://tex.z-dn.net/?f=%5Capprox%205100.88)
That's your answer
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