Answer:
Step-by-step explanation:
To calculate the amount of money in Lamar's account after 2 years with quarterly compounding interest, we can use the formula for compound interest:
\[A = P \times \left(1 + \frac{r}{n}\right)^{nt}\]
Where:
- \(A\) is the amount of money accumulated after \(t\) years, including interest.
- \(P\) is the principal amount (the initial amount of money).
- \(r\) is the annual interest rate (in decimal).
- \(n\) is the number of times interest is compounded per year.
- \(t\) is the time the money is invested for, in years.
Given:
- \(P = \$4100\)
- \(r = 1.12\% = 0.0112\) (in decimal)
- \(n = 4\) (compounded quarterly)
- \(t = 2\) years
Let's calculate:
\[A = 4100 \times \left(1 + \frac{0.0112}{4}\right)^{4 \times 2}\]
\[A = 4100 \times \left(1 + \frac{0.0112}{4}\right)^{8}\]
\[A ≈ 4100 \times (1.0028)^8\]
\[A ≈ 4100 \times 1.0224786\]
\[A ≈ 4196.64\]
So, Lamar's account will have approximately \$4196.64 after 2 years.
Now, to find out how much interest Lamar earned, we subtract the initial investment from the total amount:
\[Interest = A - P\]
\[Interest = 4196.64 - 4100\]
\[Interest ≈ 96.64\]
So, Lamar earned approximately \$96.64 in interest over 2 years.
