3 साल में आपको 50,000 रुपये मिलने वाले हैं। यदि ब्याज दर में अचानक वृद्धि हो जाती है, तो आपके लिए उस भविष्य की राशि के वर्तमान मूल्य में क्या परिवर्तन आएगा ?

1. Break Down the Problem

We need to determine how the present value (PV) of a future amount (50,000 INR) will change if the interest rate increases. To do this, we need to:

1. Calculate the present value using the formula: $PV = \frac{FV}{(1 + r)^n}$ where:
   • $FV$ = future value (50,000 INR)
   • $r$ = interest rate
   • $n$ = number of years (3 years)
2. Compare the present value at different interest rates.

2. Relevant Concepts

• Present Value Formula: $PV = \frac{FV}{(1 + r)^n}$
• The effect of interest rate on present value: As the interest rate $r$ increases, the present value $PV$ decreases.

3. Analysis and Detail

Let’s assume two scenarios for the interest rates:

• Scenario 1: $r_1 = 5\%$
• Scenario 2: $r_2 = 10\%$

Calculation for Scenario 1 ($r_1 = 5\%$):

1. Convert percentage to decimal: $r_1 = 0.05$
2. Apply the present value formula: $PV_1 = \frac{50000}{(1 + 0.05)^3} = \frac{50000}{(1.157625)} \approx 43283.64 \text{ INR}$

Calculation for Scenario 2 ($r_2 = 10\%$):

1. Convert percentage to decimal: $r_2 = 0.10$
2. Apply the present value formula: $PV_2 = \frac{50000}{(1 + 0.10)^3} = \frac{50000}{(1.331)} \approx 37594.87 \text{ INR}$

4. Verify and Summarize

Now we compare:

• Present Value at 5% Interest: $PV_1 \approx 43283.64$ INR
• Present Value at 10% Interest: $PV_2 \approx 37594.87$ INR

When the interest rate increases from 5% to 10%, the present value decreases notably.

Final Answer

If the interest rate increases, the present value of 50,000 INR to be received in 3 years will decrease from approximately 43,283.64 INR at 5% to approximately 37,594.87 INR at 10%.