Math, asked by ajay7419, 2 months ago

Mr Gupta had a recurring deposit account. He deposited 140 per month at
10% per annum. If he received 1372 as interest at the time of maturity, find
the total time for which the account was held.
tion 8​

Answers

Answered by soumili0922b
0

Answer:

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Answered by bhagyashreechowdhury
4

Given:

Mr Gupta had a recurring deposit ac count. He deposited 140 per month at

10% per annum. If he received 1372 as interest at the time of maturity, find

the total time for which the account was held.

To find:

The total time for which the ac count was held.

Solution:

To solve the above-given problem we will use the following formula:

\boxed{\bold{Interest\:on\:maturity, I = \frac{n(n+1)}{2} \times \frac{Monthly\: deposit\times Rate}{100 \times 12} }}

Here we have,

The monthly ins talment = Rs. 140

The rate of interest = 10% p.a.

The interest received at the time of maturity = Rs. 1372

Let "n" be the no. of months for which the ac count was held.

Now, on substituting the given values into the above formula of interest, we get

1372= \frac{n(n+1)}{2} \times \frac{140 \times 10}{100 \times 12} }}

\implies 1372= \frac{n(n+1)}{2} \times \frac{14 }{ 12}

\implies 1372= \frac{n(n+1)}{2} \times \frac{7 }{ 6}

\implies n(n+1) = \frac{1372 \times 2\times 6}{7}

\implies n^2 + n  =2352

\implies n^2 + n  -2352 = 0

\implies n^2 + 49n - 48n  -2352 = 0

\implies n(n+ 49)- 48 (n + 49) = 0

\implies (n+ 49)(n- 48 ) = 0

\implies n = -49 \:or\:n = 48

since the no. of months cannot be negative so we will accept only the positive value

\implies \bold{\:n = 48\:months \: or\:4\: years} . . . [since 1 year = 12 months]

Thus, the total time for which the ac count was held was → 48 months or 4 years.

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