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An annuity pays Rs.500 annually for 8 years with an interest rate of 6% compounded annually. What is the present value of the annuity?
- a)Rs.3000
- b)Rs.3500
- c)Rs.4000
- d)Rs.4500
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
An annuity pays Rs.500 annually for 8 years with an interest rate of 6...
Understanding the Present Value of an Annuity
To calculate the present value of an annuity, we use the formula:
PV = P * [(1 - (1 + r)^-n) / r]
Where:
- PV = Present Value
- P = Payment per period
- r = Interest rate per period
- n = Number of periods
Given Values
- Annual payment (P) = Rs.500
- Interest rate (r) = 6% or 0.06
- Number of years (n) = 8
Step-by-Step Calculation
1. Convert Interest Rate:
- r = 0.06
2. Substitute Values into the Formula:
PV = 500 * [(1 - (1 + 0.06)^-8) / 0.06]
3. Calculate (1 + r):
- (1 + 0.06) = 1.06
4. Calculate (1 + r)^-n:
- (1.06)^-8 ≈ 0.59345
5. Calculate 1 - (1 + r)^-n:
- 1 - 0.59345 ≈ 0.40655
6. Divide by the Interest Rate:
- 0.40655 / 0.06 ≈ 6.7758
7. Final Present Value Calculation:
- PV = 500 * 6.7758 ≈ Rs.3387.90
Rounding Off
The calculated present value of the annuity rounds to approximately Rs.3500.
Conclusion
Thus, the present value of the annuity paying Rs.500 annually for 8 years at an interest rate of 6% is approximately Rs.3500, confirming option 'B' as the correct answer.
To calculate the present value of an annuity, we use the formula:
PV = P * [(1 - (1 + r)^-n) / r]
Where:
- PV = Present Value
- P = Payment per period
- r = Interest rate per period
- n = Number of periods
Given Values
- Annual payment (P) = Rs.500
- Interest rate (r) = 6% or 0.06
- Number of years (n) = 8
Step-by-Step Calculation
1. Convert Interest Rate:
- r = 0.06
2. Substitute Values into the Formula:
PV = 500 * [(1 - (1 + 0.06)^-8) / 0.06]
3. Calculate (1 + r):
- (1 + 0.06) = 1.06
4. Calculate (1 + r)^-n:
- (1.06)^-8 ≈ 0.59345
5. Calculate 1 - (1 + r)^-n:
- 1 - 0.59345 ≈ 0.40655
6. Divide by the Interest Rate:
- 0.40655 / 0.06 ≈ 6.7758
7. Final Present Value Calculation:
- PV = 500 * 6.7758 ≈ Rs.3387.90
Rounding Off
The calculated present value of the annuity rounds to approximately Rs.3500.
Conclusion
Thus, the present value of the annuity paying Rs.500 annually for 8 years at an interest rate of 6% is approximately Rs.3500, confirming option 'B' as the correct answer.
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Community Answer
An annuity pays Rs.500 annually for 8 years with an interest rate of 6...
Use the formula for the present value of an annuity: PV = PMT * ((1 - (1 + r)^-n)/r). PV = 500 * ((1 - (1 + 0.06)^-8)/0.06) ≈ 3500.
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An annuity pays Rs.500 annually for 8 years with an interest rate of 6% compounded annually. What is the present value of the annuity?a)Rs.3000b)Rs.3500c)Rs.4000d)Rs.4500Correct answer is option 'B'. Can you explain this answer? for Commerce 2025 is part of Commerce preparation. The Question and answers have been prepared according to the Commerce exam syllabus. Information about An annuity pays Rs.500 annually for 8 years with an interest rate of 6% compounded annually. What is the present value of the annuity?a)Rs.3000b)Rs.3500c)Rs.4000d)Rs.4500Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Commerce 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An annuity pays Rs.500 annually for 8 years with an interest rate of 6% compounded annually. What is the present value of the annuity?a)Rs.3000b)Rs.3500c)Rs.4000d)Rs.4500Correct answer is option 'B'. Can you explain this answer?.
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