by-using-the-knowledge-of-sequence-and-series-show-that-the-compound-interest-is-given-by-An-P-1-RT-100-n-

Question Number 41288 by mondodotto@gmail.com last updated on 04/Aug/18

\boldsymbol by \boldsymbol using \boldsymbol the \boldsymbol knowledge \boldsymbol of

\boldsymbol sequence \boldsymbol and \boldsymbol series \boldsymbol show \boldsymbol that

\boldsymbol the \boldsymbol compound \boldsymbol interest \boldsymbol is \boldsymbol given \boldsymbol by

\boldsymbol An = \boldsymbol P {(1 + \frac{\boldsymbol RT}{100})}^{\boldsymbol n}

Answered by tanmay.chaudhury50@gmail.com last updated on 05/Aug/18

b e g i n i n g o f t h e e n d o f y e a r e n d o f y e a r

y e a r (p r i n c i p l e) - i n t e r e s t - a m o u n t

1) P_\frac{P \times R \times 1}{100} - P + \frac{P \times R \times 1}{100}

2) P (1 + \frac{R}{100}) - P (1 + \frac{R}{100}) \times \frac{R \times 1}{100} - P (1 + \frac{R}{100}) . \frac{R}{100} + P (1 + \frac{R}{100})

3) P {(1 + \frac{R}{100})}^{2} - P {(1 + \frac{R}{100})}^{2} \times \frac{R}{100} - P {1 + \frac{R}{100}}^{2} \times \frac{R}{100} + P {1 + \frac{R}{100}}^{2}

t h u s

t h u s f o r f i r s t y e a r p r i n c i p l e (p) = p a m o u n t (A) = P (1 + \frac{R}{100})

f o r 2 n d y e a r (p) = p (1 + \frac{R}{100}) a m o u n t (A) = p {(1 + \frac{R}{100})}^{2}

f o r 3 r d y e a r (p) = p {(1 + \frac{R}{100})}^{2} a m o u n t (A) = p {(1 + \frac{R}{100})}^{3}

t h u s f o r n y e a r a m o u n t (A) = p {(1 + \frac{R}{100})}^{n}