Admission to a course is increased by `15%` every year. If the number of student in this course in 1988 is `1600` . What is the expected number of students in 1990 ?

Options

A. 2080
B. 2116
C. 2356
D. 1960

Answer

To find the expected number of students in the course in 1990, we will use the formula for compound interest, as the number of students increases by a certain percentage each year.

### Step-by-Step Solution:

1. **Identify the initial values**:
- Initial number of students in 1988 (P) = 1600
- Rate of increase (R) = 15%
- Time period (n) = 1990 - 1988 = 2 years

2. **Use the compound interest formula**:
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
where:
- \(A\) = the amount after n years
- \(P\) = principal amount (initial number of students)
- \(R\) = rate of interest (percentage increase)
- \(n\) = number of years

3. **Substitute the values into the formula**:
\[ A = 1600 \left(1 + \frac{15}{100}\right)^2 \]
\[ A = 1600 \left(1 + 0.15\right)^2 \]
\[ A = 1600 \left(1.15\right)^2 \]

4. **Calculate \( (1.15)^2 \)**:
\[ (1.15)^2 = 1.3225 \]

5. **Calculate \( A \)**:
\[ A = 1600 \times 1.3225 \]
\[ A = 2116 \]

6. **Conclusion**:
The expected number of students in 1990 is **2116**.