Compound Interest Ques 17
Question
A sum of money was invested for 14 yr in scheme A which offers simple interest at a rate of 8% per annum. The amount received from scheme A after 14 yr was then invested for 2 yr in scheme B which offers compound interest (compounded annually) at a rate of 10% per annum. If the interest received from scheme B was Rs. 6678, what was the sum invested in scheme A?
(1) Rs. 15500
(2) Rs. 14500
(3) Rs. 16000
(4) Rs. 12500
(5) Rs. 15000
(IBPS RRB (Office Assistant) 2015)
Show Answer
Correct Answer: (5)
Solution: (5)
Let the principal invested in scheme A.
SI $=\frac{P\times R\times T}{100} $
$ \Rightarrow $ SI$=\frac{P\times 14\times 8}{100} $
SI $=\frac{112P}{100} $
$ A=P+SI=P+\frac{112P}{100}=\frac{212}{100}P $
On compound interest in scheme B.
$ A=\frac{212P}{100}{{( 1+\frac{10}{100} )}^{2}}=\frac{212P}{100}\times {{( \frac{110}{100} )}^{2}} $
$ =\frac{212P}{100}\times \frac{121}{100}=\frac{25652P}{10000} $
Interest received from scheme B
$ =\frac{25652P}{10000}-\frac{212P}{100A} $
$ =\frac{25652P-21200,P}{10000}=\frac{4452P}{10000} $
But given, $ \frac{4452P}{10000}=6678 $
$ P=\frac{6678\times 10000}{4452}=Rs.15000 $
BETA
