# Rs. 3600 was invested in banks X and Y at 10% simple interest and  15% compound interest respectively. If the difference between the interest received from both the banks in the 1st year is Rs 390, then find the interest received in the 2nd year.

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1. Rs. 533.33
2. Rs. 527.50
3. Rs. 566.67
4. Rs. 577.50

Option 4 : Rs. 577.50

## Detailed Solution

Given:

Total amount invested in bank X at 10% and bank Y at 15% = 3600

Difference between the two interests received from both banks for 1st year = 390

Formula used:

Simple interest = $$\dfrac{p × r × t}{100}$$

Amount(compounded) = $$p × (1 + \dfrac{r}{100})^t$$

p = principal, r = rate of interest, t = time(in years)

Solution:

Let amount invested in bank Y = k

So, the amount invested in bank X = (3600 - k)

According to the formula and given information:

Considering bank Y:

Compound interest = amount - principal

⇒ k × $$(1 + \dfrac{15}{100})^1$$ - k

⇒ ($$\dfrac{23}{20}$$ × k) - k = $$\dfrac{3k}{20}$$

Considering bank X:

Simple interest = $$\dfrac{(3600 - k) × 10 × 1}{100}$$ = $$360 - \dfrac{k}{10}$$

Difference between both the interests = 390

⇒ $$\dfrac{3k}{20}$$ -  ($$360 - \dfrac{k}{10}$$) = 390

⇒ $$\dfrac{3k + 2k}{20}$$ = 390 + 360

⇒ 5k = 15000

⇒ k = 3000

∴ Amount invested in bank Y = 3000 and bank X = 600

⇒ Interest received from X = 60 and from Y = 450 (for 1st year)

For 2nd year:

Since, simple interest remains same every year

∴ interest from bank X = 60

Total amount received from Y after 2 years = 3000 × $$(1 + \dfrac{15}{100})^2$$

⇒ 3000 × $$(\dfrac{23}{20})^2$$ = 3967.50

So, the interest received for 2nd year from Y = 967.50 - 450 = 517.50

∴ Total interest for 2nd year = 60 + 517.50 = 577.50
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