Rohit and Vinay both opened a recurring deposit account in a bank for 2 years at 8% simple interest. Vinay deposited ₹ 300 per month. On maturity, Rohit’s interest was ₹ 800 more than Vinay’s interest.
Find:
(a) interest earned by Vinay.
(b) sum deposited by Rohit every month.
(a) Time = 2 years = 24 months
Rate of interest = 8% per annum
Monthly deposit made by Vinay = ₹ 300
Interest = \frac{\mathrm{P}\times\mathrm{n}(\mathrm{n}+1)}{2}\times\frac{\mathrm{r}}{12\times100}
⇒ Interest = \frac{300\times24\times25}{2}\times\frac{8}{1200}
⇒ Interest = 300 × 300 × \frac{8}{1200}
⇒ Interest = ₹ 600
Therefore, interest earned by Vinay is ₹ 600.
(b) Interest earned by Rohit = ₹ 600 + ₹ 800 = ₹ 1400
Let Rohit deposit ₹ P per month.
⇒ 1400 = \frac{\mathrm{P}\times24\times25}{2}\times\frac{8}{1200}
⇒ 1400 = 2P
⇒ P = \frac{1400}{2} = ₹ 700
Therefore, Rohit deposits ₹ 700 per month.
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