Given:
Initial value = 400
Interest rate = 5% compounded quarterly.
To find:
The function that gives you the amount of money in dollars, J(t) in t years after the initial deposit.
Solution:
The formula for amount is:
![A=P\left(1+\dfrac{r}{n}\right)^{nt}](https://tex.z-dn.net/?f=A%3DP%5Cleft%281%2B%5Cdfrac%7Br%7D%7Bn%7D%5Cright%29%5E%7Bnt%7D)
Where, P is principal, r is the rate of interest in decimals, n is the number of times interest compounded in an year and t is the number of years.
The interest rate is 5% compounded quarterly. So, r=0.05 and n=4.
Substituting
in the above formula, we get
![A=400\left(1+\dfrac{0.05}{4}\right)^{4t}](https://tex.z-dn.net/?f=A%3D400%5Cleft%281%2B%5Cdfrac%7B0.05%7D%7B4%7D%5Cright%29%5E%7B4t%7D)
![A=400\left(1+0.0125\right)^{4t}](https://tex.z-dn.net/?f=A%3D400%5Cleft%281%2B0.0125%5Cright%29%5E%7B4t%7D)
![A=400\left(1.0125\right)^{4t}](https://tex.z-dn.net/?f=A%3D400%5Cleft%281.0125%5Cright%29%5E%7B4t%7D)
The required function notation is:
![J(t)=400\left(1.0125\right)^{4t}](https://tex.z-dn.net/?f=J%28t%29%3D400%5Cleft%281.0125%5Cright%29%5E%7B4t%7D)
Therefore, the amount of money in dollars, J(t) in t years after the initial deposit is
.