Question:
A customer has made a lumpsum investment of INR 2,00,000 with a bank. The discount rate is 15% per year. The investment enables the customer to receive a payout of INR 1,00,000 yearly for next three consecutive years.
The net present value (NPV) of his/her investment is INR ______ (rounded off to the nearest integer).
A customer has made a lumpsum investment of INR 2,00,000 with a bank. The discount rate is 15% per year. The investment enables the customer to receive a payout of INR 1,00,000 yearly for next three consecutive years.
The net present value (NPV) of his/her investment is INR ______ (rounded off to the nearest integer).
The net present value (NPV) of his/her investment is INR ______ (rounded off to the nearest integer).
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Discount each year's INR 1,00,000 payout back to present value at 15% (or use the annuity present value formula), sum them, then subtract the initial INR 2,00,000 investment.
Updated On: Aug 5, 2026
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Correct Answer: 28323
Solution and Explanation
Step 1: Understanding the Concept:
The customer pays INR 2,00,000 today and gets back INR 1,00,000 at the end of each of the next 3 years.
Because these three payouts are equal and evenly spaced, they form an annuity, so we can value them in one shot instead of discounting each year separately.
The Net Present Value (NPV) is simply the present value of what comes in minus what was paid out today.
Step 2: Key Formula or Approach:
The present value of an ordinary annuity of \( n \) equal payments \( P \) at rate \( r \) is:
\[ PV = P \times \frac{1 - (1+r)^{-n}}{r} \]
and then \( NPV = PV - C_0 \), where \( C_0 \) is the initial outlay.
Step 3: Detailed Explanation:
Here \( P = 1,00,000 \), \( r = 0.15 \), \( n = 3 \) and \( C_0 = 2,00,000 \).
First find \( (1.15)^3 = 1.520875 \), so \( (1.15)^{-3} = 0.657516 \).
\[ PV = 1,00,000 \times \frac{1 - 0.657516}{0.15} = 1,00,000 \times \frac{0.342484}{0.15} \]
\[ PV = 1,00,000 \times 2.283225 = 2,28,322.51 \]
Subtracting the initial investment:
\[ NPV = 2,28,322.51 - 2,00,000 = 28,322.51 \]
Final Answer:
Rounding to the nearest integer, the net present value works out to INR 28,323. \[ \boxed{28323} \]
The customer pays INR 2,00,000 today and gets back INR 1,00,000 at the end of each of the next 3 years.
Because these three payouts are equal and evenly spaced, they form an annuity, so we can value them in one shot instead of discounting each year separately.
The Net Present Value (NPV) is simply the present value of what comes in minus what was paid out today.
Step 2: Key Formula or Approach:
The present value of an ordinary annuity of \( n \) equal payments \( P \) at rate \( r \) is:
\[ PV = P \times \frac{1 - (1+r)^{-n}}{r} \]
and then \( NPV = PV - C_0 \), where \( C_0 \) is the initial outlay.
Step 3: Detailed Explanation:
Here \( P = 1,00,000 \), \( r = 0.15 \), \( n = 3 \) and \( C_0 = 2,00,000 \).
First find \( (1.15)^3 = 1.520875 \), so \( (1.15)^{-3} = 0.657516 \).
\[ PV = 1,00,000 \times \frac{1 - 0.657516}{0.15} = 1,00,000 \times \frac{0.342484}{0.15} \]
\[ PV = 1,00,000 \times 2.283225 = 2,28,322.51 \]
Subtracting the initial investment:
\[ NPV = 2,28,322.51 - 2,00,000 = 28,322.51 \]
Final Answer:
Rounding to the nearest integer, the net present value works out to INR 28,323. \[ \boxed{28323} \]
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