Question

Qoban has some money (M) that he divides in the ratio of 1:2. He then deposits the smaller amount in a savings scheme that offers a certain rate of interest, and the larger amount in another savings scheme that offers half of that rate of interest. Both interests compound yearly. At the end of two years, the total interest earned from the two savings schemes is £ 830. It is known that one of the interest rates is 10% and that Qoban deposited more than £1000 in each saving scheme at the start. Find the value of M?

• A. 12000
• B. 8000
• C. 6000
• D. 9000
• E. 5700

Hint:

For compound interest problems with two parts, set up separate interest calculations and sum them to form an equation. Consider both possibilities for which part gets the higher rate.

Answer 1

The Correct Option is C

Step 1: Let the two parts be $P$ and $2P$, so total $M = 3P$.
Step 2: One interest rate is 10%. Since the larger amount is in a scheme with half the rate, two cases are possible.
Step 3: Case 1: Smaller amount (P) at 10%, larger (2P) at 5%. Interest after 2 years: $P(1.1^2 - 1) + 2P(1.05^2 - 1) = 830$. $P(1.21 - 1) + 2P(1.1025 - 1) = 830$. $P(0.21) + 2P(0.1025) = 830$. $0.21P + 0.205P = 0.415P = 830 \implies P = 2000$. Then $M = 3P = 6000$. Each deposit: $P=2000$, $2P=4000$, both > 1000. This works.
Step 4: Case 2: Smaller amount (P) at 5%, larger (2P) at 10%. Interest: $P(1.05^2 - 1) + 2P(1.1^2 - 1) = 830$. $P(0.1025) + 2P(0.21) = 830$. $0.1025P + 0.42P = 0.5225P = 830 \implies P \approx 1588.5$. Then $M \approx 4765.5$, not an options and also not matching the condition that one rate is 10% (both rates are 10% and 5% in this case, so it's valid but M is not in optionss).
Step 5: Since 6000 is in the optionss and satisfies all conditions, it is the correct answer.
Step 6: Final Answer: The value of M is 6000.