A deposit earns simple interest. Its value is Rs. 4,500 after 1 year and Rs. 6,000 after 4 years. Determine the original deposit and the yearly interest rate.

Correct Answer: Principal = 4,000, Rate = 12.5%

Step-by-step explanation:

Step 1: Understand the Simple Interest Concept
In simple interest, the interest earned each year remains constant because it is always calculated on the initial principal amount. The total value of an investment after a given period equals the original principal plus the total simple interest accumulated during that time.

Let:

The original deposit (Principal) = $P$

The simple interest earned per year = $I$

The annual interest rate = $R$

From the given information, we can set up two linear equations:

Value of the deposit after 1 year:

$P+I=\mathrm{4,500}$   — (Equation 1)

Value of the deposit after 4 years:

$P+4I=\mathrm{6,000}$   — (Equation 2)

Step 2: Determine the Interest Earned Per Year ($I$)
Subtract Equation 1 from Equation 2 to find the interest accumulated over the 3-year gap (from year 1 to year 4):

$(P+4I)-(P+I)=\mathrm{6,000}-\mathrm{4,500}$

$3I=\mathrm{1,500}$

Now, divide by 3 to calculate the interest earned in a single year:

$I=\frac{\mathrm{1,500}}{3}=500$

The simple interest earned each year is Rs. 500.

Step 3: Calculate the Original Deposit ($P$)
Substitute the yearly interest $I=500$ back into Equation 1:

$P+500=\mathrm{4,500}$

$P=\mathrm{4,500}-500=\mathrm{4,000}$

Thus, the original deposit (Principal) is Rs. 4,000.

Step 4: Calculate the Yearly Interest Rate ($R$)
The standard formula for simple interest is:

$I=\frac{P\times R\times T}{100}$

Substitute the known values for 1 year ($I=500$, $P=\mathrm{4,000}$, and $T=1$):

$500=\frac{\mathrm{4,000}\times R\times 1}{100}$

$500=40\times R$

Solve for $R$:

$R=\frac{500}{40}=12.5\%$

Final Answer:
The original deposit is Rs. 4,000 and the yearly interest rate is 12.5%.