Arithmetic

Simple & Compound Interest

Medium

Anindita invests a total of $1$ lakh rupees distributed across three schemes A, B and C for a period of two years. These schemes offer an interest rate of $10\%$ , $8\%$ and $12\%$ per annum, respectively, each compounded annually. If the initial investment amount in scheme A is $30000$ rupees and the total interest earned from all the three schemes during the first year is $10600$ rupees, then the total interest earned, in rupees, from all the three schemes for the second year is

$10308$

$11748$

$22348$

$19708$

✅ Correct Option: 2

Since the investment in scheme A is $₹30,000$ and total investment is $₹1,00,000$ :

Investment in B + Investment in C $= ₹1,00,000 - ₹30,000$

$= ₹70,000$

Let investment in B $= ₹x$ , then investment in C $= ₹(70,000 - x)$

For compound interest, first-year interest equals simple interest on principal:

Interest from

A $= 30,000 \times \dfrac{10}{100}$

$= ₹3,000$

Interest from B

$= x \times \dfrac{8}{100}$

$= ₹0.08x$

Interest from C

$= (70,000 - x) \times \dfrac{12}{100}$

$= ₹0.12(70,000 - x)$

Using the given first year total interest of $₹10,600$ :

$3,000 + 0.08x + 0.12(70,000 - x) = 10,600$

$3,000 + 0.08x + 8,400 - 0.12x = 10,600$

$11,400 - 0.04x = 10,600$

$0.04x = 800$

$x = 20,000$

Therefore: Investment in B $= ₹20,000$ , Investment in C $= ₹50,000$

For second year interest, we calculate on (Principal + First year interest):

Amount at end of first year:

Scheme A:

$30,000 + 3,000 = ₹33,000$

Scheme B:

$20,000 + 1,600 = ₹21,600$

Scheme C:

$50,000 + 6,000 = ₹56,000$

Second year interest:

From A:

$33,000 \times \dfrac{10}{100} = ₹3,300$

From B:

$21,600 \times \dfrac{8}{100} = ₹1,728$

From C:

$56,000 \times \dfrac{12}{100} = ₹6,720$

Total second year interest $= 3,300 + 1,728 + 6,720 = ₹11,748$

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