The rate of interest on a sum of money for the first two years is 6% p.a., for the next two years it is 7% p.a. and 8% p.a. for the period exceeding four years, all at simple interest. If a person earns an interest of 7,536 by the end of the seven years, what is the amount at the end of the period of investment?

Options

A. 15072
B. 11304
C. 22608
D. 21308

Answer

To solve the problem step by step, we will calculate the total interest earned over the seven years based on the different interest rates for each period and then find the principal amount (P). Finally, we will calculate the total amount at the end of the investment period.

### Step 1: Calculate the interest for the first two years at 6% per annum.
- Formula: \( \text{Interest} = \frac{P \times R \times T}{100} \)
- Here, \( R = 6\% \) and \( T = 2 \) years.
- Interest for the first two years:
\[ I_1 = \frac{P \times 6 \times 2}{100} = \frac{12P}{100} = 0.12P \]

### Step 2: Calculate the interest for the next two years at 7% per annum.
- Here, \( R = 7\% \) and \( T = 2 \) years.
- Interest for the next two years:
\[ I_2 = \frac{P \times 7 \times 2}{100} = \frac{14P}{100} = 0.14P \]

### Step 3: Calculate the interest for the last three years at 8% per annum.
- Here, \( R = 8\% \) and \( T = 3 \) years.
- Interest for the last three years:
\[ I_3 = \frac{P \times 8 \times 3}{100} = \frac{24P}{100} = 0.24P \]

### Step 4: Calculate the total interest earned over the seven years.
- Total interest \( I \) is the sum of all the interests calculated:
\[ I = I_1 + I_2 + I_3 = 0.12P + 0.14P + 0.24P = 0.50P \]

### Step 5: Set the total interest equal to the given interest earned.
- We know from the problem statement that the total interest earned is \( 7536 \):
\[ 0.50P = 7536 \]

### Step 6: Solve for \( P \).
- Rearranging the equation gives:
\[ P = \frac{7536}{0.50} = 15072 \]

### Step 7: Calculate the total amount at the end of the investment period.
- The total amount \( A \) is given by:
\[ A = P + I = P + 7536 \]
- Substituting the value of \( P \):
\[ A = 15072 + 7536 = 22608 \]

### Final Answer:
The amount at the end of the period of investment is **22608**.

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