Question

arjuna deposit Rs.2000 per month in a bank for 18 months in a reccuring deposit account. if he gets Rs. 40000 at the time of maturity. what is the rate of interest per annum. ​

Answer 1

Answer :-

The rate of interest is 14.03 or 14(after round - off)

Given :-

◍ Principal (P) = Rs. 2000

◍ Time (n) = 18 months

◍ Maturity value (M) = Rs. 40000

To find :-

• The rate of interest (R)

Solution :-

As principal and time are given, we will find the total deposited amount first.

$\boxed{Total \: \: deposited \: \: amount = P\times n} \\ \\ = Rs. 2000 \times 18 \\ \\ = Rs. 36000$

◉ Maturity value is the sum of total deposited amount and simple interest.

$\boxed{ \tt{ \mapsto \: Maturity \: \: value = T.D.A. + S.I.}}$

Substituting the values we have in the above given formula,

Rs. 40000 = Rs. 36000 + S.I.

Rs. 40000 - Rs. 36000 = S.I.

Rs. 4000 = S.I.

Now, we have the value of simple interest and by using this value we will find rate of interest.

$\boxed{ \tt{ \mapsto \: S.I. = P \times \frac{n(n + 1)}{2 \times 12} \times \frac{r}{100} } }$

Solving it.

$= > 4000 = 2000\times \frac{18(18 + 1)}{2 \times 12} \times \frac{r}{100} \\ \\ = > 4000 = 2000\times \frac{18 \times 19}{2 \times 12} \times \frac{r}{100} \\ \\ = > 4000 = 28500\times \frac{r}{100} \\ \\ = > 4000 = 285\times r\\ \\ = > \frac{4000}{285} = r \\ \\ = > 14.03 = r$

The rate of interest is 14.03 or 14 (after round - off).