What is the compound interest earned on Rs. 80,000 at 40% per annum in one year, compounded quarterly? Option 1: Rs. 28317 Option 2: Rs. 37128 Option 3: Rs. 18732 Option 4: Rs. 21387

Answer: Rs. 37128. Solution: Given: Principal = Rs. 80,000 Interest Rate = 40% per annum Time Period = 1 year Compounding = Quarterly (4 times a year) For quarterly compounding, the year is divided into 4 equal quarters, so interest is calculated and added 4 times in 1 year. Rate per quarter = (40%)/4 = 10% Number of compounding periods = 1 x 4 = 4 Using the compound interest formula A = P(1 + r/100)^n where: P = 80,000 r = 10% (rate per quarter) n = 4 (number of quarters) A = 80,000 x (1 + 10/100)^4 A = 80,000 x (1.1)^4 Calculating (1.1)^4: (1.1)^2 = 1.21 (1.1)^4 = 1.21 x 1.21 = 1.4641 Therefore: A = 80,000 x 1.4641 A = 1,17,128 Compound Interest = Final Amount - Principal CI = 1,17,128 - 80,000 CI = 37,128 Therefore, the compound interest earned is Rs. 37,128.

Arithmetic

Simple & Compound Interest

Medium

What is the compound interest earned on Rs. 80,000 at 40% per annum in one year, compounded quarterly?

Rs. 28317

Rs. 37128

Rs. 18732

Rs. 21387

✅ Correct Option: 2

Given:

Principal = Rs. 80,000

Interest Rate = 40% per annum

Time Period = 1 year

Compounding = Quarterly (4 times a year)

For quarterly compounding, the year is divided into 4 equal quarters, so interest is calculated and added 4 times in 1 year.

Rate per quarter $= \dfrac{40\%}{4} = 10\%$

Number of compounding periods $= 1 \times 4 = 4$

Using the compound interest formula $A = P(1 + \dfrac{r}{100})^n$ where:

$P = 80,000$

$r = 10\%$ (rate per quarter)

$n = 4$ (number of quarters)

$A = 80,000 \times (1 + \dfrac{10}{100})^4$

$A = 80,000 \times (1.1)^4$

Calculating $(1.1)^4$ :

$(1.1)^2 = 1.21$

$(1.1)^4 = 1.21 \times 1.21 = 1.4641$

Therefore:

$A = 80,000 \times 1.4641$

$A = 1,17,128$

Compound Interest $=$ Final Amount $-$ Principal

$CI = 1,17,128 - 80,000$

$CI = 37,128$

Therefore, the compound interest earned is Rs. 37,128.

2025: 20 May Shift 2

Consider the compound interest in the following cases:

(A) The compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly is Rs. 2500

(B) The compound interest on Rs 2800 at 10% per annum for 18 months is Rs. 434.

Choose the correct statement(s):

2023: 7 June Shift 1

A sum of Rs 10,000 becomes Rs 14,400 on compound interest in 2 years. What is the rate of interest per annum ?

2026: 30 May Shift 2

Consider the simple interest of the following

(A) A sum of Rs 200 at 6% per annum for 5 yr.

(B) A sum of Rs 2000 at $13\frac{1}{2}$ % per annum for 4 yr.

(D) A sum of Rs 68000 at $16\frac{2}{3}$ % per annum for 9 months.

Arrange the above in descending order.

Choose the correct answer from the options given below:

2025: 14 May Shift 2

A certain sum becomes 3-fold at 4% annual rate of interest. At what rate, will it become 6-fold?

2025: 2 June Shift 2

A sum of ₹ 5500 is lent out in two parts in such a way that the interest on one part at 12% for 4 years is equal to that on another part at 8% for 5 years. What will be the two parts of the sum?

2026: 20 May Shift 2

A sum of ₹ 80,000 is invested at 6% p.a. at simple interest for the first year, then 8% p.a. for the next 2 years (still simple interest). What is the total interest earned over the 3 year period?

What is the compound interest earned on Rs. 80,000 at 40% per annum in one year, compounded quarterly?

Solution

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