simple interest and compound interest
on what sum will the compound interest at 10% per annum for 3 years compounded annually be Rs 331?
To find the principal amount for compound interest, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated amount (compound interest + principal)
P = Principal amount
r = Rate of interest (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
In this case, we are given:
A = Rs 331
r = 10% per annum = 0.1 (in decimal form)
n = 1 (compounded annually)
t = 3 years
Using the formula, we can rearrange it to solve for P:
P = A / (1 + r/n)^(nt)
Now, let's substitute the given values:
P = 331 / (1 + 0.1/1)^(1*3)
Simplifying further:
P = 331 / (1 + 0.1)^3
P = 331 / (1.1)^3
P = 331 / 1.331
Therefore, the principal amount will be approximately Rs 248.65 when the compound interest at 10% per annum for 3 years compounded annually is Rs 331.
x(1.10)^3 = x + 331
x(1.1)^3 - x = 331
x(1.1^3 - 1) = 331
x = 331/(1.1^3 - 1) = 1000
check:
1000(1.1^3) = 1331
so the increase (or interest) is 331