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Given annuity of 100 amount to 3137.12 at 4.5%p.a C. I. The number of year will be?
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Given annuity of 100 amount to 3137.12 at 4.5%p.a C. I. The number of ...
Calculation of Number of Years in Annuity



  • Given annuity amount = 100

  • Final value of annuity = 3137.12

  • Interest rate = 4.5% p.a.

  • We can use the formula for future value of annuity to calculate the number of years:



Formula:

FV = P * [((1 + r)^n - 1) / r]



  • FV = final value of annuity

  • P = periodic payment (annuity amount)

  • r = interest rate per period

  • n = number of periods



Solution:

Substituting the given values in the formula:


3137.12 = 100 * [((1 + 0.045)^n - 1) / 0.045]


Simplifying the equation:


31.3712 = ((1.045^n - 1) / 0.045)


Multiplying both sides by 0.045:


1.4117 = 1.045^n - 1


Adding 1 to both sides:


2.4117 = 1.045^n


Taking logarithm of both sides:


log(2.4117) = n * log(1.045)


Dividing both sides by log(1.045):


n = log(2.4117) / log(1.045) ≈ 29.8


Answer:

The number of years in the annuity is approximately 29.8 years.
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Given annuity of 100 amount to 3137.12 at 4.5%p.a C. I. The number of year will be?
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Given annuity of 100 amount to 3137.12 at 4.5%p.a C. I. The number of year will be? 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 Given annuity of 100 amount to 3137.12 at 4.5%p.a C. I. The number of year will be? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given annuity of 100 amount to 3137.12 at 4.5%p.a C. I. The number of year will be?.
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