Final answer:
To find the time it takes for ₹5400 to yield ₹1373.76 as compound interest at 12% per annum, we can use the compound interest formula. Plugging in the given values and solving the equation, we find that it takes approximately 4.01 years.
Step-by-step explanation:
To find the time it takes for ₹5400 to yield ₹1373.76 as compound interest at 12% per annum, we can use the compound interest formula:
Compound Interest = P(1 + r/n)^(nt) - P
where P is the principal amount (initial amount), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
Plugging in the given values, we get:
₹1373.76 = ₹5400(1 + 0.12/1)^(1*t) - ₹5400
Simplifying the equation:
₹1373.76 = ₹5400(1.12)^t - ₹5400
Adding ₹5400 to both sides:
₹6773.76 = ₹5400(1.12)^t
Dividing both sides by ₹5400:
1.25 = 1.12^t
Taking the natural logarithm of both sides:
ln(1.25) = ln(1.12^t)
Using the property of logarithms (ln(a^b) = b*ln(a)):
ln(1.25) = t*ln(1.12)
Dividing both sides by ln(1.12):
t = ln(1.25) / ln(1.12)
Using a calculator, we find that t is approximately 4.01 years.