Consider the compound interest of the following

(A) The compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly is: Rs 2522

(B) The compound interest on Rs 2800 at 10% per annum for 18 months, compounded annually is: Rs 434

Choose the correct statement(s):

Statement (A): Rs 16,000 at 20% p.a. for 9 months, compounded quarterly

When interest is compounded quarterly, it is calculated and added to the principal 4 times a year (every 3 months).

Principal (P) = Rs 16,000

Annual Rate = 20%

Quarterly Rate (r) = 20% ÷ 4 = 5% = 0.05

Time = 9 months = 3 quarters

Number of times compounded (n) = 3

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Amount (A) = P(1 + r)ⁿ

$A = 16,000 \times (1 + 0.05)^3$

$A = 16,000 \times (1.05)^3$

$A = 16,000 \times 1.157625$

$A = 18,522$

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Compound Interest = Amount - Principal

$CI = 18,522 - 16,000$

$CI = 2,522$

Statement (A) is correct.

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Statement (B): Rs 2,800 at 10% p.a. for 18 months, compounded annually

When compounded annually with fractional years, compound interest applies for complete years and simple interest applies on the amount for the remaining fractional year.

Principal (P) = Rs 2,800

Rate (r) = 10% per annum

Time = 18 months = 1 year + 6 months

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For the first complete year:

$A_1 = P(1 + r)$

$A_1 = 2,800 \times (1 + 0.10)$

$A_1 = 2,800 \times 1.10$

$A_1 = 3,080$

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For the remaining 6 months, simple interest applies on Rs 3,080:

$SI = P \times r \times t$

$SI = 3,080 \times 0.10 \times 0.5$

$SI = 154$

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Final Amount = 3,080 + 154 = 3,234

Compound Interest = Amount - Principal

$CI = 3,234 - 2,800$

$CI = 434$

Statement (B) is correct.

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Both statements (A) and (B) are correct.