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

Question

Answer

Calculation of Number of Years in Annuity

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

Formula:

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

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.