MathsICSE Class 8 · Simple and Compound Interest

Half-Yearly Compound Interest: Halve the Rate, Double the Periods (ICSE Class 8)

Updated 17 October 2026 · Fact-checked

When interest is compounded half-yearly, the rate per period is $\frac{R}{2}\%$ and the number of periods is $2n$, so $A = P\left(1 + \frac{R}{200}\right)^{2n}$. The CISCE limit is up to 3 half-yearly steps (1 year 6 months).

Understand Half-Yearly Compound Interest

"Compounded half-yearly" means interest is calculated and added to the principal every six months. The annual rate $R %$ is shared equally: each half-year earns $\frac{R}{2} %$ .

Conversion rule.

Rate per period $= \frac{R}{2} %$ per half-year.
Number of periods $= 2 \times$ (years). For 1 year there are $2$ periods; for $1 \frac{1}{2}$ years, $3$ periods. The curriculum allows up to 3 steps only.

$ $A = P (1 + \frac{R}{200})^{2 n}, C I = A - P .$ $

Why more than yearly? Interest is added sooner, so it starts earning interest earlier. For example, 20% per annum on Rs 10,000 gives Rs 12,000 compounded yearly but $10000 \times 1. 1^{2} =$ Rs 12,100 compounded half-yearly, a gain of Rs 100.

Common slip. Halve the rate and double the time; doing only one is the standard mistake. Do not use $\frac{R}{2}$ with $n$ years or $R$ with $2 n$ periods.

Reverse problems. If the compound interest or the amount for one year is given, write $A = P (1 + r)^{2}$ with $r = \frac{R}{200}$ and solve for $P$ by dividing: $P = \frac{C I}{( 1 + r ) ^{2} - 1}$ .

Checking. With 3 periods, expand year by year: each period multiplies by the same factor, so $(1 + r)^{3}$ is the product of three equal factors.

Half-Yearly Compound Interest: formulas to remember

Half-yearly amount: $A = P (1 + \frac{R}{200})^{2 n}$; Rate per period is $R /2$ , periods $2 n$ .
Period count: $periods = 2 \times years$; Up to 3 in Class VIII.
Principal from CI (1 year): $P = \frac{C I}{( 1 + r ) ^{2} - 1}, r = \frac{R}{200}$; Reverse use of the formula.

How to solve Half-Yearly Compound Interest questions

Convert to half-year units first: halve the rate, double the time.

1Find the rate per half-year: $\frac{R}{2} %$ .
2Find the number of half-years: $2 n$ .
3Compute the factor $1 + \frac{R}{200}$ and raise it to $2 n$ .
4Multiply by $P$ for the amount, subtract $P$ for the interest.
5Compare with the yearly result if asked.

Half-Yearly Compound Interest in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Savings account with six-monthly credit

Suppose a savings account pays 12% per annum with interest credited every six months, and you deposit Rs 5,000 for one year.

Find the interest earned.

Try it first, then show the solutionSolution

Rate per half-year $= 6%$ , periods $= 2$ .
$A = 5000 \times 1.0 6^{2} = 5000 \times 1.1236 = 5618$ ; interest $= 618$ .

Answer: Rs 618.

Memory hook: Halve the rate, double the periods.

Tricks to remember Half-Yearly Compound Interest

Short memory aids. Say each one aloud once, then use it on a question the same day.

Halve and double
Half-yearly: rate becomes R/2, years become 2n.
Use it when: Every half-yearly question.
Count the steps
1 year = 2 steps, 1.5 years = 3 steps; stop there for Class VIII.
Use it when: Choosing the exponent.

Half-Yearly Compound Interest: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Reading the period · 1 mark · MCQBoard level

Rs 4,000 is invested at 10% per annum compounded half-yearly for 1 year. The amount is:
(a) Rs 4,400 (b) Rs 4,410 (c) Rs 4,420 (d) Rs 4,200

Try it first, then show the solutionSolution

Rate per half-year $5%$ , 2 periods: $4000 \times 1.0 5^{2} = 4000 \times 1.1025 = 4410$ .

Answer: (b)

Example 2: Basic half-yearly sum · 3 marks · Short answerBoard level

Find the compound interest on Rs 5,000 at 12% per annum for 1 year, compounded half-yearly.

Try it first, then show the solutionSolution

Rate per half-year $= 6%$ ; periods $= 2$ .
$A = 5000 \times 1.0 6^{2} = 5000 \times 1.1236 = 5618$ .
$C I = 5618 - 5000 = 618$ .

Answer: Rs 618

Example 3: Yearly versus half-yearly · 3 marks · Short answerHarder board level

Rs 10,000 is invested for 1 year at 20% per annum. How much more does it earn if interest is compounded half-yearly instead of yearly?

Try it first, then show the solutionSolution

Yearly: $10000 \times 1.20 = 12000$ .
Half-yearly: $10000 \times 1.1 0^{2} = 10000 \times 1.21 = 12100$ .
Difference $= 12100 - 12000 = 100$ .

Answer: Rs 100 more

Example 4: One and a half years · 4 marks · Short answerHarder board level

Find the amount and compound interest on Rs 7,500 for $1 \frac{1}{2}$ years at 20% per annum, compounded half-yearly.

Try it first, then show the solutionSolution

Rate per period $10%$ ; periods $= 3$ .
$1. 1^{3} = 1.331$ ; $A = 7500 \times 1.331 = 9982.50$ .
$C I = 9982.50 - 7500 = 2482.50$ .

Answer: Amount Rs 9,982.50; CI Rs 2,482.50

Example 5: Finding the principal · 4 marks · Long answerHOTS / competency

The compound interest for 1 year on a sum at 8% per annum, compounded half-yearly, is Rs 816. Find the sum, and how much more this is than simple interest for the same year.

Try it first, then show the solutionSolution

Rate per period $4%$ : $(1.04)^{2} - 1 = 1.0816 - 1 = 0.0816$ .
$P = \frac{816}{0.0816} = 10000$ .
$S I = \frac{10000 \times 8 \times 1}{100} = 800$ .
CI exceeds SI by $816 - 800 = 16$ .

Answer: Sum Rs 10,000; CI is Rs 16 more

Where students lose marks in Half-Yearly Compound Interest

The slips examiners see most often, and what to write instead.

Mistake: Halving the rate but not doubling the time
Both conversions are needed together.
Wrong working
$A = 5000 \times 1.0 6^{1} = 5300$ .
Right working
$A = 5000 \times 1.0 6^{2} = 5618$ .
Do this: Write "rate/2, time x 2" before substituting.
Usually costs: Answer and method marks.
Mistake: Using the full annual rate each half-year
Each period earns half the annual rate.
Wrong working
$A = 5000 \times 1.1 2^{2} = 6272$ .
Right working
$A = 5000 \times 1.0 6^{2} = 5618$ .
Do this: Compare with the yearly result: half-yearly is only slightly bigger.
Usually costs: Answer mark.

Exam tips

Check the result is slightly more than the yearly compounding answer.
Show the factor (like 1.1236) so errors in powering are easy to trace.
The curriculum limit is up to 3 half-yearly steps.

Practice questions on Half-Yearly Compound Interest

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
If the annual rate is 14%, the rate per half-year in half-yearly compounding is:
(a) 28% (b) 14% (c) 7% (d) 3.5%
Hint
Split the annual rate equally over two halves.
Answer
(c)
Q2 · 3 marks · Short answerBoard level
Find the compound interest on Rs 20,000 at 10% per annum for 1 year, compounded half-yearly.
Hint
5% for 2 periods.
Answer
$A = 20000 \times 1.0 5^{2} = 20000 \times 1.1025 = 22050$ ; $C I = 2050$ .
Q3 · 3 marks · Short answerHarder board level
Find the amount on Rs 30,000 for 1 year at 8% per annum, compounded half-yearly, and the compound interest.
Hint
4% per half-year.
Answer
$1.0 4^{2} = 1.0816$ ; $A = 30000 \times 1.0816 = 32448$ ; $C I = 2448$ .
Q4 · 4 marks · Short answerHarder board level
Find the amount and compound interest on Rs 12,500 for $1 \frac{1}{2}$ years at 12% per annum, compounded half-yearly.
Hint
Three periods at 6%.
Answer
$1.0 6^{2} = 1.1236$ , $1.0 6^{3} = 1.191016$ . $A = 12500 \times 1.191016 = 14887.70$ ; $C I = 2387.70$ .
Q5 · 4 marks · Long answerHOTS / competency
On Rs 50,000 for 1 year at 12% per annum, compare compound interest compounded yearly with compounded half-yearly. Find the difference.
Hint
Compute both amounts.
Answer
Yearly: $50000 \times 1.12 = 56000$ . Half-yearly: $50000 \times 1.0 6^{2} = 50000 \times 1.1236 = 56180$ . Difference $= 180$ , in favour of half-yearly compounding.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.Rate per half-year for annual rate R?Show answer
R/2.
2.Number of periods in 1.5 years half-yearly?Show answer
3.
3.Half-yearly amount formula?Show answer
P(1 + R/200)^(2n).
4.Which is larger for the same P, R, n: yearly or half-yearly compounding?Show answer
Half-yearly.

Half-Yearly Compound Interest: frequently asked questions

Why not use R/2 with n years?

Because the interest is added twice a year, so there are 2n additions each at R/2.

Does half-yearly compounding change simple interest?

No; simple interest has no compounding.