Mary Brown invested an amount of 4,000 in Fund A at a rate of 6% per annum simple interest...
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Mary Brown invested an amount of $4,000 in Fund A at a rate of 6% per annum simple interest for a period of 6 years. The interest earned is further invested in two other funds, B and C, for 5 years in the ratio 1:2.
The rate of simple interest in Fund B is 8%, and the difference between the amounts received as simple interest from Funds C and B is $288. What is the rate of interest for Fund C?
Show answer & explanation
The interest from Fund A is $1,440, split between Funds B and C as $480 and $960. Fund B earns $192, and since Fund C's interest exceeds Fund B's by $288, Fund C earns $480, giving a 10% rate.
Step-by-step Derivation:
Step 1: Calculate the simple interest from Fund A.
SI_A = 4000 × 0.06 × 6 = $1,440.
Step 2: Divide this interest between Funds B and C in the ratio 1:2.
Total parts = 1 + 2 = 3.
Amount in Fund B = 1440 × (1/3) = $480.
Amount in Fund C = 1440 × (2/3) = $960.
Step 3: Calculate interest from Fund B at 8% for 5 years.
SI_B = 480 × 0.08 × 5 = $192.
Step 4: Use the difference of $288 to find Fund C's interest.
SI_C - SI_B = 288 ⇒ SI_C = 288 + 192 = $480.
Step 5: Solve for Fund C's rate.
SI_C = 960 × r × 5 = 480.
4800r = 480 ⇒ r = 0.10 = 10%.