Question

Mrs Sharma opened a recurring deposit Rs.1800 per month for two and half years. If she received Rs.59580 at the time of maturity, find the rate of interest per annum.​

Answer 1

Answer:

8% per annum

5580×4/2790

Answer 2

The rate of interest per annum = 8%

Given :

• Mrs. Sharma opened a recurring deposit Rs. 1800 per month for two and half years.

• Mrs. Sharma received Rs.59580 at the time of maturity

To find :

The rate of interest per annum

Solution :

Step 1 of 3 :

Calculate interest received by Mrs. Sharma

Mrs. Sharma opened a recurring deposit Rs. 1800 per month for two and half years.

Mrs. Sharma received Rs. 59580 at the time of maturity

Instalment per month = P = Rs. 1800

Number of months = n

= Two and half years

= 30 months

Total amonut deposited

= Rs. 1800 × 30

= Rs. 54000

Maturity value = Rs. 59580

We know that ,

Maturity value = Total amonut deposited + Interest

∴ Interest

= Rs. 59580 - Rs. 54000

= Rs. 5580

Step 2 of 3 :

Form the equation to calculate rate of interest per annum

Let rate of interest per annum = r%

So by the given condition

$\displaystyle \sf \frac{P \times n(n + 1)}{2 \times 12} \times \frac{r}{100} = Interest$

$\displaystyle \sf{ \implies } \frac{1800 \times 30 \times (30 + 1)}{2 \times 12} \times \frac{r}{100} = 5580$

Step 3 of 3 :

Calculate rate of interest per annum

$\displaystyle \sf \frac{1800 \times 30 \times (30 + 1)}{2 \times 12} \times \frac{r}{100} = 5580$

$\displaystyle \sf{ \implies }\frac{1800 \times 30 \times 31}{2 \times 12} \times \frac{r}{100} = 5580$

$\displaystyle \sf{ \implies }\frac{18 \times 30 \times 31 \times r}{24} = 5580$

$\displaystyle \sf{ \implies }r = 5580 \times \frac{24}{18 \times 30 \times 31}$

$\displaystyle \sf{ \implies }r = 5580 \times \frac{24}{18 \times 30 \times 31}$

$\displaystyle \sf{ \implies }r = 8$

Hence rate of interest per annum = 8%

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