Question

Mr. Ravi opens a recurring deposit account of ?800 per month. How many installments does he have to pay to get a maturity amount of ?20600. The rate of interest paid is 7% per annum.

Answer 1

Dear student
$$\begin{gathered} Letthenumberofmonthlyinstalments=n \\ Now,Principal,P=Rs800,Rate,R=7\% \\ Interest=P\times \frac{n\left(n+1\right)}{24}\times \frac{R}{100} \\ \Rightarrow Interest=\frac{800\times n\left(n+1\right)\times 7}{24\times 100}=Rs\left[\frac{7n(n+1)}{3}\right] \\ Now,moneydeposited+Interest=Maturityvalue \\ 800\times n+\frac{7n(n+1)}{3}=20600 \\ \Rightarrow 800n+\frac{7n(n+1)}{3}=20600 \\ \Rightarrow 2400n+7n^2+7n=61800 \\ \Rightarrow 7n^2+2407n-61800=0 \\ \Rightarrow 7n^2-168n+2575n-61800=0 \\ \Rightarrow 7n\left(n-24\right)+2575\left(n-24\right)=0 \\ \Rightarrow \left(n-24\right)\left(7n+2575\right)=0 \\ \Rightarrow n-24=0or7n+2575=0 \\ \Rightarrow n=24orn=-\frac{2575}{7}\left(rejected\right) \\ So,numberofmonthlyinstalments=24 \end{gathered}$$
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