Find the compound interest if an amount of 50,000 is deposited in bank for one year at the rate of 8% per annum compounded semi-annually.

Option b: 4,080. Solution: Derivation of Compound Interest Given: - Principal (P) = text{Rs. }50,000 - Rate of Interest (r) = 8% per annum compounded semi-annually - Time (t) = 1 year Step 1: Calculate periodic rate (i) and number of periods (n) - Periodic rate i = r/2 = 8%/2 = 4% = 0.04 per half-year. - Number of periods n = t x 2 = 1 x 2 = 2 half-years. Step 2: Calculate Future Value (A) and Compound Interest (CI) A = P(1 + i)^n A = 50000(1 + 0.04)^2 A = 50000(1.04)^2 A = 50000 x 1.0816 = text{Rs. }54,080 CI = A - P = 54080 - 50000 = text{Rs. }4,080 Hence, Option B is the correct answer.

Find the compound interest if an amount of $50,000$ is deposited in bank for one year at the rate of $8\%$ per annum compounded semi-annually.

The correct answer is Option b: $4,080$. **Derivation of Compound Interest** Given: - Principal ($P$) = $\text{Rs. }50,000$ - Rate of Interest ($r$) = $8\%$ per annum compounded semi-annually - Time ($t$) = $1$ year **Step 1: Calculate periodic rate ($i$) and number of periods ($n$)** - Periodic rate $i = \frac{r}{2} = \frac{8\%}{2} = 4\% = 0.04$ per half-year. - Number of periods $n = t \times 2 = 1 \times 2 = 2$ half-years. **Step 2: Calculate Future Value ($A$) and Compound Interest ($CI$)** $$A = P(1 + i)^n$$ $$A = 50000(1 + 0.04)^2$$ $$A = 50000(1.04)^2$$ $$A = 50000 \times 1.0816 = \text{Rs. }54,080$$ $$CI = A - P = 54080 - 50000 = \text{Rs. }4,080$$ Hence, **Option B** is the correct answer.

Mathematics for FinancePYQ Nov 20Question 1208 of 512

All Questions

Find the compound interest if an amount of $\displaystyle 50,000$ is deposited in bank for one year at the rate of $\displaystyle 8\%$ per annum compounded semi-annually.

Options

\displaystyle 3,080

\displaystyle 4,080

\displaystyle 3,456

\displaystyle 7,856

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Correct Answer

✅ Option b — $\displaystyle 4,080$

All Options:

A $\displaystyle 3,080$
B $\displaystyle 4,080$
C $\displaystyle 3,456$
D $\displaystyle 7,856$

Detailed Solution & Explanation

**Derivation of Compound Interest** Given: - Principal (

\displaystyle P

) =

\displaystyle \text{Rs. }50,000

- Rate of Interest (

\displaystyle r

) =

\displaystyle 8\%

per annum compounded semi-annually - Time (

\displaystyle t

) =

\displaystyle 1

year **Step 1: Calculate periodic rate (

\displaystyle i

) and number of periods (

\displaystyle n

)** - Periodic rate

\displaystyle i = \frac{r}{2} = \frac{8\%}{2} = 4\% = 0.04

per half-year. - Number of periods

\displaystyle n = t \times 2 = 1 \times 2 = 2

half-years. **Step 2: Calculate Future Value (

\displaystyle A

) and Compound Interest (

\displaystyle CI

)**

A = P(1 + i)^n

A = 50000(1 + 0.04)^2

A = 50000(1.04)^2

A = 50000 \times 1.0816 = \text{Rs. }54,080

CI = A - P = 54080 - 50000 = \text{Rs. }4,080

Hence, **Option B** is the correct answer.

Key Concepts to Understand

Compound Interest

Interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods.

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Find the compound interest if an amount of 50,000\displaystyle 50,00050,000 is deposited in bank for one year at the rate of 8%\displaystyle 8\%8% per annum compounded semi-annually.