A person invested 1100 rs in a company at compound interest compounded semi-annually.he received rs 1331 after one year.rate% is?
answer rate 20%
poorly worded question,
so the amount is 1331 rs, then
1100(1+i)^2 = 1331
(1+i)^2 = 1.21
1+i = √1.21 = 1.1
i = .1 or 10%
so the annual rate is 20%
let the semi-annual rate be i
amount after 1 year = 1100(1 + i)^2
interest = 1100(1 + i)^2 - 1100 = 1331
1100(1 + i)^2 = 2431
(1+i)^2 = 2.21
1+i = √2.21 = appr 1.4866
i = .4866
WOW, annual rate is .4866(2) = .9732 or 97% ?????
check: 1100(1.4866..)^2 = 2430.98
interest = 1330.98 or 1331 rs
Seems unreasonable high to me, do you have a typo ??
To find the rate of interest, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (1331 Rs in this case)
P = the principal amount (1100 Rs in this case)
r = the annual interest rate (to be determined)
n = the number of times interest is compounded per year (in this case, semi-annually, so it is 2)
t = the time in years (1 year in this case)
Let's substitute the given values into the formula:
1331 = 1100(1 + r/2)^(2*1)
Simplifying the equation:
1331/1100 = (1 + r/2)^2
1.210909 = (1 + r/2)^2
Taking the square root of both sides:
√1.210909 = 1 + r/2
1.100381 ≈ 1 + r/2
Now, subtracting 1 from both sides:
1.100381 - 1 = r/2
0.100381 = r/2
Now, multiplying both sides by 2:
0.100381 * 2 = r
r ≈ 0.200762 or 20.0762%
Therefore, the rate of interest is approximately 20.08%.