Question

Q. 4. Karim deposits 150 per month in a
recurring deposit account for 2 years. Find the
amount he will get at the time of maturity at
the rate of 5% p.a.


​

Answer 1

Given :

• Principal = Rs.150
• Time = 2 years
• Rate = 5% p.a.

To Find :

The amount Karim will get at the time of maturity.

Solution :

Here the concept of recurring deposit is used. Under this scheme, an investor deposits a fixed amount every month for a specified number of months and on expiry period he gets the amount deposited by him together with the interest due to him. The amount received by the investor on the expiry period is called maturity value.

Explanation :

Here,

n = number of months for which the money is deposited = 2 × 12 = 24 months

The interest on the recurring deposit can be calculated by using this formula,

$\boxed{\bf I=P\times\dfrac{n(n+1)}{2\times12}\times\dfrac{r}{100}}$

where,

• I = Interest
• P = Principal = Rs.150
• n = Time = 24 months
• r = Rate = 5% p.a.

Substituting the values,

$\\ :\implies\sf I=150\times\dfrac{24(24+1)}{2\times12}\times\dfrac{5}{100}$

$\\ :\implies\sf I=150\times\dfrac{24\times25}{2\times12}\times\dfrac{\not{5}}{\cancel{100}\ \ \ ^{20}}$

$\\ :\implies\sf I=15\!\!\!\not{0}\times\dfrac{24\times25}{2\times12}\times\dfrac{1}{2\!\!\!\not{0}}$

$\\ :\implies\sf I=15\times\dfrac{\cancel{24}\ \ \ ^2\times25}{2\times\cancel{12}}\times\dfrac{1}{2}$

$\\ :\implies\sf I=15\times\dfrac{\not{2}\times25}{2\times1}\times\dfrac{1}{\not{2}}$

$\\ :\implies\sf I=15\times\dfrac{1\times25}{2\times1}\times\dfrac{1}{1}$

$\\ :\implies\sf I=15\times\dfrac{25}{2}$

$\\ :\implies\sf I=15\times12.5$

$\\ :\implies\sf I=187.5$

$\\ \therefore\boxed{\bf I=Rs.187.5.}$

Interest = Rs.187.5.

Now,

We know that,

Maturity Value = P × n + I

where,

• P = Rs.150
• n = 24 months
• I = Rs.187.5

Substituting the values,

⇒ MV = (150 × 24) + 187.5

⇒ MV = 3600 + 187.5

⇒ MV = 3787.5

∴ Maturity Value = Rs.3787.5

Amount Karim will get at the time of maturity is Rs.3787.5