A sum of money was invested for 14 years was in Scheme A which offers simple interest at a rate of 8% p.a. The amount received from Scheme… — Answer & Discussion

A sum of money was invested for 14 years was in Scheme A which offers simple interest at a rate of 8% p.a. The amount received from Scheme A after 14 years was then invested for two years in Scheme B which offers compound interest (compounded annually) at a rate of 10% p.a. If the interest received from Scheme B was Rs. 6,678, what was the sum invested in Scheme A?

ARs. 15,500
BRs. 14,500
CRs. 16,500
DRs. 12,500

Answer not set

Join the discussion Report an error

Discussion 1

CCommunity22 May 2019

Solution
Let the sum invested in scheme A = $Rs. 100x$
Time = 14 years and rate = 8% under simple interest
=> $S.I. = \frac{P \times R \times T}{100}$
= $\frac{100x \times 8 \times 14}{100} = 112x$
=> Amount invested in Scheme B = $100x + 112x = Rs. 212x$
Time = 2 years and rate = 10% under compound interest.
$C.I. = P [(1 + \frac{R}{100})^T - 1]$
=> $6678 = 212x [(1 + \frac{10}{100})^2 - 1]$
=> $6678 = 212x [(\frac{11}{10})^2 - 1] = 212x (\frac{21}{100})$
=> $0.21x = \frac{6678}{212} = 31.5$
=> $x = \frac{31.5}{0.21} = 150$
$\therefore$ Sum invested in scheme A = $100 \times 150 = Rs. 15,000$