c) Subhadra has a recurring deposit account in ABCD bank. She deposits Rs. 800 per month and
gets Rs.15198 as maturity value. If the rate of interest is 7 p.c.p.a, find the total time for which
the account was held.
Answers
Solution :-
Let us assume that, the total time was x years.
so,
→ x years = 12x months .
now,
→ principal for first month = 800 * 12x * (12x + 1) / 2 = 4800x(12x + 1) .
then,
→ Interest = [{4800x(12x + 1)} * 7 * 1]/(100 *12) = 28x(12x + 1)
now,
→ Actual sum deposit = 12x * 800 = 9600x .
therefore,
→ Maturity amount = Actual sum deposit + Interest
→ 15198 = 9600x + 28x(12x + 1)
→ 15198 = 9600x + 336x² + 28x
→ 336x² + 9628x - 15198 = 0
→ 2(168x² + 4814x - 7599) = 0
→ 168x² + 4814x - 7599 = 0
→ 168x² - 252x + 5066x - 7599 = 0
→ 84x(2x - 3) + 2533(2x - 3) = 0
→ (2x - 3)(84x + 2533) = 0
→ x = (3/2) or (-2533/84) .
since negative value of x is not possible.
therefore, the total time for which the account was held was (3/2) or 1(1/2) or 1 year 6 months .
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