Question

Mr. Nair opened a recurring deposit account in a bank and deposited rs. 400 per month for three years. if he received rs. 2220 as interest at the time of maturity, then the rate of interest per annum is :​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

• Mr. Nair opened a recurring deposit account in a bank and deposited Rs. 400 per month for three years and he received Rs. 2220 as interest at the time of maturity.

So, We have

• Interest received on maturity, I = Rs 2220

• Time = 3 year = 36 months.

• So, number of instâllment, n = 36

• Amount deposited per month, P = Rs 400

Let assume that

• Rate of interest be r % per annum.

We know that

Interest, I on instâllment of Rs P invested for n months at the rate of r % per annum is given by

$\blue\bigstar \: \red{\boxed{\mathbf{I \: = \: \dfrac{n \: (n \: + \: 1)P}{24 } \times \dfrac{r}{100} }}}$

where,

• I = Interest received on maturity

• P = Amount of monthly instâllment

• r = rate of interest per annum

• n = number of monthly instâllment.

So, using the formula, we get

$\rm :\longmapsto\:2220\: = \: \dfrac{36 \: (36 \: + \: 1) \times 400}{24 } \times \dfrac{r}{100}$

$\rm :\longmapsto\:2220\: = \: \dfrac{36 \times 37 \times 4}{24 } \times r$

$\rm :\longmapsto\:2220\: = \: \dfrac{3 \times 37 \times 4}{2} \times r$

$\rm :\longmapsto\:2220\: = \: \dfrac{3 \times 37 \times 2}{1} \times r$

$\rm :\longmapsto\:2220 = 37 \times 2 \times r$

$\rm :\longmapsto\:1110 = 37 \times r$

$\bf\implies \:r \: = \: 10 \: \% \: per \: annum$

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Additional Information :-

Amount, A on instâllment of Rs P invested for n months at the rate of r % per annum is given by

$\blue\bigstar \: \red{\boxed{\mathbf{A \: = \: nP \: + \: \dfrac{n \: (n \: + \: 1)P}{24 } \times \dfrac{r}{100} }}}$

where,

A = Amount received on maturity or maturity value

P = Amount of monthly instâllment

r = rate of interest per annum

n = number of monthly instâllment.