Answer:
Interest earned = $3546.50
Option B is correct option.
Step-by-step explanation:
Time t = 20 years
Principal Amount P =$3815.24
Interest r = 3.3% or 0.033
Compounded quarterly n = 4
We need to find How much interest has Lucas earned?
First we need to find the future value in the account after 20 years
The formula used to find future value A is: ![A=P(1+\frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
Putting values of t, r , n and P to find A i.e future value
![A=P(1+\frac{r}{n})^{nt}\\A=3815.24(1+\frac{0.033}{4})^{20*4} \\Simplifying:\\A=3815.24(1+0.00825)^{20*4} \\A=3815.24(1.00825)^{80}\\A=3815.24(1.929)\\A= 7361.74](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D%5C%5CA%3D3815.24%281%2B%5Cfrac%7B0.033%7D%7B4%7D%29%5E%7B20%2A4%7D%20%5C%5CSimplifying%3A%5C%5CA%3D3815.24%281%2B0.00825%29%5E%7B20%2A4%7D%20%5C%5CA%3D3815.24%281.00825%29%5E%7B80%7D%5C%5CA%3D3815.24%281.929%29%5C%5CA%3D%207361.74)
Now finding interest amount by subtracting the initial deposit from the future value
Interest earned = Future Value (A)- Initial Deposit (P)
Interest earned = 7,361.74 - 3815.24
Interest earned = 3546.50
So, Lucas have earned interest = $3546.50
Option B is correct option.