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The present value of annuity of Rs.5,000 per annum for 12 years at 4% p.a C.I. annually is a) Rs.46,000 b) Rs.46,850 c) Rs.15,000 d) none of these?
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The present value of annuity of Rs.5,000 per annum for 12 years at 4% ...
Solution:
Concept: The present value of an annuity is the sum of the present values of all the payments due under the annuity.
Calculation:
Given,
Annuity amount = Rs. 5,000 per annum for 12 years
Rate of interest = 4% p.a C.I. annually
Let us first calculate the future value of annuity, and then we will find the present value of the same.
Calculation of Future Value:
Using the formula for the future value of an annuity, we get:
FV = A[(1 + r)n - 1]/r
where,
A = annuity amount = Rs. 5,000 per annum
r = rate of interest per annum = 4% p.a C.I. annually
n = number of years = 12
Substituting the values, we get:
FV = 5000[(1 + 0.04)^12 - 1]/0.04
FV = Rs. 81,138.10 (approx)
Calculation of Present Value:
Using the formula for the present value of an annuity, we get:
PV = A[(1 - (1 + r)^-n)/r]
where,
A = annuity amount = Rs. 5,000 per annum
r = rate of interest per annum = 4% p.a C.I. annually
n = number of years = 12
Substituting the values, we get:
PV = 5000[(1 - (1 + 0.04)^-12)/0.04]
PV = Rs. 46,850.59 (approx)
Therefore, the present value of the annuity is Rs. 46,850.59 (approx).
Hence, the correct option is (b) Rs. 46,850.
Concept: The present value of an annuity is the sum of the present values of all the payments due under the annuity.
Calculation:
Given,
Annuity amount = Rs. 5,000 per annum for 12 years
Rate of interest = 4% p.a C.I. annually
Let us first calculate the future value of annuity, and then we will find the present value of the same.
Calculation of Future Value:
Using the formula for the future value of an annuity, we get:
FV = A[(1 + r)n - 1]/r
where,
A = annuity amount = Rs. 5,000 per annum
r = rate of interest per annum = 4% p.a C.I. annually
n = number of years = 12
Substituting the values, we get:
FV = 5000[(1 + 0.04)^12 - 1]/0.04
FV = Rs. 81,138.10 (approx)
Calculation of Present Value:
Using the formula for the present value of an annuity, we get:
PV = A[(1 - (1 + r)^-n)/r]
where,
A = annuity amount = Rs. 5,000 per annum
r = rate of interest per annum = 4% p.a C.I. annually
n = number of years = 12
Substituting the values, we get:
PV = 5000[(1 - (1 + 0.04)^-12)/0.04]
PV = Rs. 46,850.59 (approx)
Therefore, the present value of the annuity is Rs. 46,850.59 (approx).
Hence, the correct option is (b) Rs. 46,850.
Community Answer
The present value of annuity of Rs.5,000 per annum for 12 years at 4% ...
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The present value of annuity of Rs.5,000 per annum for 12 years at 4% p.a C.I. annually is a) Rs.46,000 b) Rs.46,850 c) Rs.15,000 d) none of these?
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The present value of annuity of Rs.5,000 per annum for 12 years at 4% p.a C.I. annually is a) Rs.46,000 b) Rs.46,850 c) Rs.15,000 d) none of these? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The present value of annuity of Rs.5,000 per annum for 12 years at 4% p.a C.I. annually is a) Rs.46,000 b) Rs.46,850 c) Rs.15,000 d) none of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The present value of annuity of Rs.5,000 per annum for 12 years at 4% p.a C.I. annually is a) Rs.46,000 b) Rs.46,850 c) Rs.15,000 d) none of these?.
The present value of annuity of Rs.5,000 per annum for 12 years at 4% p.a C.I. annually is a) Rs.46,000 b) Rs.46,850 c) Rs.15,000 d) none of these? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The present value of annuity of Rs.5,000 per annum for 12 years at 4% p.a C.I. annually is a) Rs.46,000 b) Rs.46,850 c) Rs.15,000 d) none of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The present value of annuity of Rs.5,000 per annum for 12 years at 4% p.a C.I. annually is a) Rs.46,000 b) Rs.46,850 c) Rs.15,000 d) none of these?.
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