Question 1: A person opens a recurring deposit account with a Bank  and deposited 600 per month for 20 months. Calculate the maturity value of this account, if the bank pays interest at the rate of 10% per annum.

Maturity value for the recurring deposits = Total Sum of Money deposited + Interest earned on it

$P =$ Amount deposited every month

$n =$ number of months the deposits were made

$r\% =$ rate of interest

$P = Rs. \ 600, \ n = 20, \ r = 10\%$

Maturity Value $= P \times n + P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$= 600 \times 20 + 600 \times$ $\frac{20(20+1)}{2 \times 12}$ $\times$ $\frac{10}{100}$ $= Rs. 13050$

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Question 2: A person  opened a Recurring Deposit Account in a certain bank and deposited Rs. 640 per month for 4 ½ years. Find the maturity value of this account, if the bank pays interest at the rate of 12% per year.

$P = Rs. \ 640$, no of months $= 54, \ r = 12\%$

Maturity Value $= P \times n + P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$= 640 \times 54 +640 \times$ $\frac{54(54+1)}{2 \times 12}$ $\times$ $\frac{12}{100}$ $= Rs. 44064$

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Question 3: Person A and Person B both opened recurring bank account in a bank, if A deposited Rs. 1200 per month for 3 years and B deposited Rs. 1500 per month for 2 ½ years; find, on maturity, who will get more amount and by how much? The rate of interest paid by the bank is 10% per annum.

For Person A

$P = Rs. \ 1200$, no of months $= 36, \ r = 10\%$

Maturity Value $= P \times n + P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$=1200 \times 36 +1200 \times$ $\frac{36(36+1)}{2 \times 12}$ $\times$ $\frac{10}{100}$ $= Rs. 49860$

For Person B

$P = Rs. \ 1500$ , no of months $= 30, \ r = 10\%$

Maturity Value $= P \times n + P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$=1500 \times 30 +1500 \times$ $\frac{30(30+1)}{2 \times 12}$ $\times$ $\frac{10}{100}$ $= Rs. 50812.5$

B will get more amount. The difference is $50812.5-49860 = Rs. \ 952.5$

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Question 4: A person deposited a certain sum of money every month in a recurring deposit account for a period of 12 months. If the bank pays interest at the rate of 11% p.a. and he gets  Rs. 12715 as the maturity value of this account, what sum of money did he pay every month?

$P = Rs. \ x,$, no of months $= 12, \ r = 11\%$ Maturity Amount $= Rs. 12715$

Maturity Value $= P \times n + P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$12715 =x \times 12 +x \times$ $\frac{12(12+1)}{2 \times 12}$ $\times$ $\frac{11}{100}$

$x(12+$ $\frac{12 \times 13}{2 \times 12}$ $\times$ $\frac{11}{100}$ $) = 12715 \Rightarrow x = Rs. 1000$

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Question 5: A man has recurring deposit account in a bank for 3 ½ years. If the rate of interest is 12% p.a. and the man gets  Rs. 10205 on maturity, find the value of monthly installment.

$P = Rs. \ x,$, no of months $= 42, \ r = 12\%$ Maturity Amount $= Rs. 10205$

Maturity Value $= P \times n + P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$10205 =x \times 42 +x \times$ $\frac{42(42+1)}{2 \times 12}$ $\times$ $\frac{12}{100}$

$x(42+$ $\frac{42 \times 43}{2 \times 12}$ $\times$ $\frac{12}{100}$ $) = 10205 \Rightarrow x = Rs. 200$

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Question 6: Explain the following:

i) Punnet has a recurring deposit account in Bank of Baroda and deposits Rs. 140 per month for 4 years. If he gets Rs. 8092 on maturity, find the rate of interest given by the bank.

ii) David opened a recurring deposit account in a bank and deposited Rs. 300 per month for two years. If he received Rs. 7725 at the time of maturity, find the rate of interest per annum. [2008]

i)

$P = Rs. \ 140$, no of months $= 48, \ rate = r\%$ Maturity Amount $= Rs. 8092$

Maturity Value $= P \times n + P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$8092 =140 \times 48 +140 \times$ $\frac{48(48+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$r =$ $\frac{(8092-140 \times 48) \times (2 \times 12) \times 100}{140 \times 48 \times 49}$ $\Rightarrow r=10\%$

ii)

$P = Rs. \ 300$, no of months $= 24, \ rate = r\%$ Maturity Amount $= Rs. 7725$

Maturity Value $= P \times n + P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$7725 =300 \times 24 +300 \times$ $\frac{24(24+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$r =$ $\frac{(7725-300 \times 24) \times (2 \times 12) \times 100}{300 \times 24 \times 25}$ $\Rightarrow r=7\%$

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Question 7: Amit deposited 150 per month in a bank for 8 month under the recurring deposit scheme. What will be the maturity value of his deposits, if the rate of interest is 8% per annum and interest is calculated at the end of every month? [2001, 2007]

$P = Rs. \ 150$, no of months $= 8, \ r = 8\%$

Maturity Value $= P \times n + P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times \frac{r}{100}$

$=150 \times 8 +150 \times$ $\frac{8(8+1)}{2 \times 12}$ $\times$ $\frac{8}{100}$ $= Rs. 1236$

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Question 8: A person deposited Rs. 350 per month in a bank for 1 year and 3 months under the recurring deposit scheme. If the maturity value of her deposits is Rs. 5565; find the rate of interest per annum.

$P = Rs. \ 350$, no of months $= 15, \ rate = r\%$ Maturity Amount $= Rs. 5565$

Maturity Value $= P \times n + P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$5565 =350 \times 15 +350 \times$ $\frac{15(15+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$r =$ $\frac{(5565-350 \times 15) \times (2 \times 12) \times 100}{350 \times 15 \times 16}$ $\Rightarrow r=9\%$

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Question 9: A recurring deposit account of Rs. 1200 per month has a maturity value of Rs. 12440. If the rate of interest is 8% and the interest is calculated at the end of every month; find the time (in months) of this recurring deposit account.

$P = Rs. \ 1200$, no of months $= n, \ rate = 8\%$ Maturity Amount $= Rs. 12440$

Maturity Value $= P \times n + P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$12440 =1200 \times n +1200 \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{8}{100}$

$12440 = 1200n + 4n(n+1)$

or $n^2+301n-3110=0 \Rightarrow n = 10 \ or -311$

Hence $n = 10$ months.

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Question 10: A person has a recurring deposit account of Rs. 300 per month. If the rate of interest is 12% and the maturity value of this account is Rs. 8100; find the time (in years) of this recurring deposit account.

$P = Rs. \ 300$, no of months $= n, \ rate = 12\%$ Maturity Amount $= Rs. 8000$

Maturity Value $= P \times n + P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$

$8100 =300 \times n +300 \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{12}{100}$

$8100 = 300n +$ $\frac{3}{2}$ $n(n+1)$

or $1.5n^2+301.5n-8100=0 \Rightarrow n = 24 \ or -225$

Hence $n = 24$ months or $2$ years.

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Question 11: Gupta opened a recurring deposit account in a bank. He deposited Rs. 2500 per month for two years. At the time of maturity, he got Rs. 67500. Find:

The total interest earned by Mr. Gupta

The rate of interest per annum. [2010]

$P = Rs. \ 2500$, no of months $= 24, \ rate = r\%$ Maturity Amount $= Rs. 67500$
Maturity Value $= P \times n + P \times$ $\frac{n(n+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$
$67500 =2500 \times 24 +2500 \times$ $\frac{24(24+1)}{2 \times 12}$ $\times$ $\frac{r}{100}$
$r =$ $\frac{(67500-2500 \times 24) \times (2 \times 12) \times 100}{2500 \times 24 \times 25}$ $\Rightarrow r=12\%$
Interest $=2500 \times$ $\frac{24(24+1)}{2 \times 12}$ $\times$ $\frac{12}{100}$ $= Rs. \ 7500$