Question

(a) Rita has an RD Account of ₹ 800 per month. If the rate of interest is 6% p.a and she receives ₹ 1,200 as interest at the time of maturity, find (i) the time for this RD Account. (ii) the amount of maturity.​

Answer 1

Answer:

this ans is 40 now

Step-by-step explanation:

how are you

Answer 2

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

Rita has an RD Account of ₹ 800 per month.

The rate of interest is 6% p.a.

She receives ₹ 1,200 as interest at the time of maturity.

$\large\underline{\sf{To\:Find - }}$

( i ) The time for RD account

( ii ) Amount he will get on maturity

Formulas used:–

The interest received on a sum of money Rs P invested every month at the rate of r % per annum for n months is

$\bold{ \red {\boxed{\text{I} = \text{P} \times \dfrac{ \text{n(n + 1)}}{2 \times 12} \times \dfrac{ \text{r}}{100} }}}$

AND

$\bold{ \red {\boxed{\text{Maturity \: value} = \text{nP} + \text{I} }}}$

where,

• • I = Interest

• • P = Sum invested per month

• • n = number of months

• • r = Rate

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

Given that,

Rita has an RD Account of ₹ 800 per month.

The rate of interest is 6% p.a.

She receives ₹ 1,200 as interest at the time of maturity

So, we have

Sum invested per month, P = ₹ 800

Rate of interest, r = 6 % per annum

Interest received, I = ₹ 1200

Let assume that the number of months be 'n'.

So, by using the formula,

$\rm :\longmapsto\:I = \text{P} \times \dfrac{ \text{n(n + 1)}}{2 \times 12} \times \dfrac{ \text{r}}{100}$

$\rm :\longmapsto\:1200 = \text{800} \times \dfrac{ \text{n(n + 1)}}{2 \times 12} \times \dfrac{ \text{6}}{100}$

$\rm :\longmapsto\:1200 = 2n(n + 1)$

$\rm :\longmapsto\:600 = n(n + 1)$

$\rm :\longmapsto\: {n}^{2} + n = 600$

$\rm :\longmapsto\: {n}^{2} + n - 600 = 0$

$\rm :\longmapsto\: {n}^{2} +30 n - 20n- 600 = 0$

$\rm :\longmapsto\:n(n + 30) - 20(n + 30) = 0$

$\rm :\longmapsto\:(n - 20)(n + 30) = 0$

$\rm :\longmapsto\:n - 20 = 0 \: \: \: or \: \: \: n + 30 = 0$

$\bf\implies \:n = 20$

So, it means the time of RD account is for 20 months.

Now,

We have

Sum invested per month, P = ₹ 800

Interest received on maturity, I = ₹ 1200

Number of months, n = 20

We know,

$\bold{ \red {\boxed{\text{Maturity \: value} = \text{nP} + \text{I} }}}$

So,

$\rm :\longmapsto\:Maturity \: value \: = \: 20 \times 800 + 1200$

$\rm :\longmapsto\:Maturity \: value \: = \: 16000 + 1200$

$\rm :\longmapsto\:Maturity \: value \: = \: 17200$

So, Rita received ₹ 17200 on maturity.