The annual payment X 160 in 5 yr at 5% per annum simple interest will discharge a debt of

Options

A. X980
B. X880
C. X440
D. X220

Answer

To solve the problem step by step, we will use the formula for annual payment in the context of simple interest.

### Step 1: Understand the Given Information
- Annual payment (A) = 160
- Time (T) = 5 years
- Rate of interest (R) = 5% per annum

### Step 2: Use the Formula for Annual Payment
The formula for annual payment (A) in terms of principal (P), time (T), and rate (R) is:

\[ A = \frac{100P}{100T + RT(T-1)/2} \]

### Step 3: Substitute the Known Values into the Formula
Substituting the values we have into the formula:

\[ 160 = \frac{100P}{100 \times 5 + 5 \times 5 \times (5 - 1)/2} \]

### Step 4: Simplify the Denominator
Calculate the denominator step by step:

1. Calculate \(100 \times 5 = 500\)
2. Calculate \(5 \times 5 = 25\)
3. Calculate \((5 - 1) = 4\)
4. Calculate \(25 \times 4 = 100\)
5. Divide by 2: \(\frac{100}{2} = 50\)

Now, add these two results together:

\[ 500 + 50 = 550 \]

### Step 5: Rewrite the Equation
Now we can rewrite the equation:

\[ 160 = \frac{100P}{550} \]

### Step 6: Cross-Multiply to Solve for P
Cross-multiply to isolate P:

\[ 160 \times 550 = 100P \]

### Step 7: Calculate the Left Side
Calculate \(160 \times 550\):

\[ 160 \times 550 = 88000 \]

### Step 8: Solve for P
Now, divide both sides by 100 to find P:

\[ P = \frac{88000}{100} = 880 \]

### Step 9: Conclusion
Thus, the debt that will be discharged is:

\[ \text{Debt} = 880 \]