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

by using the knowledge of

sequence and series show that

the compound interest is given by

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