The difference between compound interest and simple interest on a certain amount for1.5 yes at 12% per annum is ₹ 150.calculate the amount.
x[(1.12)^(3/2) - (1.12)] = 150
assuming compounding annually
Plz send me answers
To calculate the amount for which the difference between compound interest and simple interest is ₹150, we need to use the formulas for compound interest and simple interest.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
The formula for simple interest is:
A = P + (P * r * t)
Given:
Principal amount (P) = ?
Annual interest rate (r) = 12% per annum = 12/100 = 0.12
Number of years (t) = 1.5 years
Difference between compound interest and simple interest = ₹150
Let's solve for the principal amount (P):
1) Using the compound interest formula:
A(compound interest) = P(1 + r/n)^(nt)
A(compound interest) = P(1 + 0.12/1)^(1 * 1.5)
2) Using the simple interest formula:
A(simple interest) = P + (P * r * t)
A(simple interest) = P + (P * 0.12 * 1.5)
Now, we can set up the equation using the given difference:
A(compound interest) - A(simple interest) = ₹150
P(1 + 0.12/1)^(1 * 1.5) - [P + (P * 0.12 * 1.5)] = ₹150
Simplifying the equation, we get:
P * [(1.12)^(1.5)] - P - (P * 0.18) = ₹150
Combine the terms with P:
[(1.12)^(1.5) - 1 - 0.18] * P = ₹150
Solve for P:
[(1.12)^(1.5) - 1 - 0.18] * P = ₹150
P = ₹150 / [(1.12)^(1.5) - 1 - 0.18]
Using a calculator or a spreadsheet program, you can calculate the value of P. The principal amount (P) will give you the final answer or amount for which the difference between compound interest and simple interest is ₹150.