Question

The formula to find compound amount, if the interest is compounded half yearly

Answer 1

The formula to find compound amount, if the interest is compounded half yearly__________ answer to this question is here

Answer 2

Answer:

Compounded amount, A, with Principal amount, P, at an annual interest rate, R, compounded half yearly, after Period T

A = P[1 + ($\frac{R}{2}$ x $\frac{1}{100}$) x T]

Step-by-step explanation:

If interest is compounded half yearly,

Principal Amount = P

Annual rate of interest = R.

Half yearly effective interest rate = R / 2.

Compounded amount, A, after six months i.e. Period 1

= P + P x $\frac{R}{2}$ x $\frac{1}{100}$  = P(1 + $\frac{R}{2}$ x $\frac{1}{100}$)

Compounded amount, A, after one year i.e. Period 2  

= P(1 + $\frac{R}{2}$ x $\frac{1}{100}$) + P x $\frac{R}{2}$ x $\frac{1}{100}$

= P(1 +  $\frac{R}{2}$ x $\frac{1}{100}$ + $\frac{R}{2}$ x $\frac{1}{100}$) = P[1 + ($\frac{R}{2}$ x $\frac{1}{100}$) x 2]

Compounded amount, A, after one and a half years i.e. Period 3

= P[1 + ($\frac{R}{2}$ x $\frac{1}{100}$) x 2] + P x $\frac{R}{2}$ x $\frac{1}{100}$ = P[1 + ($\frac{R}{2}$ x $\frac{1}{100}$) x 2 + ($\frac{R}{2}$ x $\frac{1}{100}$)]

= P[1 + ($\frac{R}{2}$ x $\frac{1}{100}$) x 3]

Therefore, Compounded amount, A, after i.e. Period T

= P[1 + ($\frac{R}{2}$ x $\frac{1}{100}$) x T]