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प्रश्न
The maturity value of an R.D. Account is ₹ 16176. If the monthly instalment is ₹ 400 and the rate of interest is 8%; find the time (period) of this R.D Account.
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उत्तर
Installment per month (P) = Rs. 400
Number of months (n) = n
Let rate of interest (r) = 8% p.a.
∴ `S.I. = P xx (n(n + 1))/(2 xx 12) xx r/100`
= `400 xx (n(n + 1))/24 xx 8/100`
= Rs. `(4n(n + 1))/3`
Maturity value = Rs. (400 × n) + Rs. `(4n(n + 1))/3`
Given maturity value = Rs. 16,176
Then Rs. (400 × n) + Rs. `(4n(n + 1))/3` = Rs. 16,176
⇒ 1200n + 4n2 + 4n = Rs. 48,528
⇒ 4n2 + 1204n = Rs. 48,528
⇒ n2 + 301n – 12132 = 0
⇒ (n + 337)(n – 36) = 0
⇒ n = –337 or n = 36
Then number of months = 36 months
= 3 years
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| Ist April 2007 | By Cash | - | 8550.00 | 8550.00 |
| 12th- April 2007 | To Self | 1200.00 | -- | 7350.00 |
| 24th April 2007 | By Cash | - | 4550.00 | 11900.00 |
| 8th July 2007 | By Cheque | - | 1500.00 | 13400.00 |
| 10th Sept. 2007 | By Cheque | - | 3500.00 | 16900.00 |
| 17th Sept. 2007 | By Cheque | 2500.00 | - | 14400.00 |
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