When Interest is Compounded Half Yearly -
Let principal = $ P, Rate = R % p.a, and Time = n years
Then, principal = $ P, Rate = R/2 % half yearly and Time = 2n half years.
R
Amount = $ { P X ( 1 + ---------- )²ⁿ }
2 X 100
Example.1) At what rate per cent annum per annum will a sum of $ 4000 yield, $ 1324 as compound interest in 3 years ?
Ans.) Principal = $ 4000, C.I = $ 1324, and Time = 3 years.
So, amount in 3 years = $ (4000 + 1324) = $ 5324
R
Amount = $ { P X ( 1 + -------- )ⁿ }
100
(100 + R)ᶟ
5324 = { 4000 X ------------ }
100ᶟ
(100 + R)ᶟ 5324 1331 11ᶟ
=> ------------ = ----------- = ---------- = -------
100ᶟ 4000 1000 10ᶟ
100 + R 11
=> ---------- = --------
100 10
100 + R = 110
R = 110 – 100 = 10%
Hence the required rate is 10% (Ans.)