Each of A and B both opened recurring deposit accounts in a bank. If A deposited Rs1,200 per month for 3 years and B deposited Rs1,500 per month for 2.5 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. Options: A, Rs812.50 B, Rs952.50 B, Rs860.50 Both of them get the same amount
Question
Each of A and B both opened recurring deposit accounts in a bank. If A deposited ₹1,200 per month for 3 years and B deposited ₹1,500 per month for 2.5 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.
Options:
- A, ₹812.50
- B, ₹952.50
- B, ₹860.50
- Both of them get the same amount
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Answer
The correct option is B $$ \text { B, ₹ 952.50} $$
Calculation for A:
- Installment per month (P): ₹ 1,200
- Number of months (n): $3 \times 12 = 36$ months
- Total Amount Deposited: $$ 36 \times 1200 = ₹ 43,200 $$
- Rate of interest (r): 10% per annum
Simple Interest (S.I.) Calculation:
$$ \begin{array}{rl} \text{S.I.} & = P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100} \ & = 1200 \times \frac{36(36+1)}{2 \times 12} \times \frac{10}{100} \ & = 1200 \times \frac{1332}{24} \times \frac{10}{100} \ & = ₹ 6660 \end{array} $$
Maturity Value for A:
$$ \begin{array}{r} \text{Total Amount Deposited} + \text{Interest} \ = ₹ 43,200 + ₹ 6,660 \ = ₹ 49,860 \end{array} $$
Calculation for B:
- Installment per month (P): ₹ 1,500
- Number of months (n): $2.5 \times 12 = 30$ months
- Total Amount Deposited: $$ 30 \times 1500 = ₹ 45,000 $$
- Rate of interest (r): 10% per annum
Simple Interest (S.I.) Calculation:
$$ \begin{array}{rl} \text{S.I.} & = P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100} \ & = 1500 \times \frac{30(30+1)}{2 \times 12} \times \frac{10}{100} \ & = 1500 \times \frac{930}{24} \times \frac{10}{100} \ & = ₹ 5812.50 \end{array} $$
Maturity Value for B:
$$ \begin{array}{r} \text{Total Amount Deposited} + \text{Interest} \ = ₹ 45,000 + ₹ 5812.50 \ = ₹ 50,812.50 \end{array} $$
Comparison:
- B gets more amount than A.
- Difference in Maturity Amount: $$ ₹ 50,812.50 - ₹ 49,860 = ₹ 952.50 $$
Therefore, B gets ₹ \mathbf{952.50} more than A.
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