Simple Interest: Formula, Calculation & Applications: 17 MCQs with answers

A · The original principal only

Simple interest is charged only on the original principal $P$; it never earns interest on interest, which is what makes it 'simple'.

B · $SI = \frac{P \times R \times T}{100}$

The rate is a percentage, so it is divided by 100: $SI = \frac{P \times R \times T}{100}$.

D · Years

The rate is per annum (per year), so time must be expressed in years before substituting.

D · $P + SI$

The amount is what you finally have or repay: principal plus simple interest, $A = P + SI$.

A · ₹1,440

$SI = \frac{8000 \times 6 \times 3}{100} = \frac{144000}{100} = ₹1{,}440$.

A · A short-term moneylender loan

Simple interest is the standard method for short-term loans, moneylender loans and simple savings schemes; long-term products usually use compound interest.

A · True

Simple interest is computed only on the principal using $SI = \frac{P \times R \times T}{100}$, where $T$ must be in years.

A · ₹250

Six months is $T = 0.5$ years, so $SI = \frac{5000 \times 10 \times 0.5}{100} = ₹250$. Plugging in $T = 6$ would wrongly give ₹3,000.

D · 6%

$R = \frac{100 \times SI}{P \times T} = \frac{100 \times 1200}{10000 \times 2} = 6\%$ per annum.

A · Because the rate is a percentage, so $R\% = \frac{R}{100}$

The rate $R$ is given as a percent, and $R\% = \frac{R}{100}$ converts it into a decimal multiplier.

B · Doubles

$SI$ is directly proportional to $T$ when $P$ and $R$ are fixed, so doubling the time doubles the interest.

C · $P = \frac{100 \times SI}{R \times T}$

Multiply both sides by 100 and divide by $R \times T$: $P = \frac{100 \times SI}{R \times T}$.

C · Simple gives ₹3,000; compound gives ₹3,310

Simple interest adds a fixed ₹1,000 each year (total ₹3,000). Compound interest earns on the growing balance: ₹1,000 + ₹1,100 + ₹1,210 = ₹3,310.

C · Time was used in months instead of years

The formula needs $T$ in years. Six months is $0.5$ years, giving $SI = \frac{5000 \times 10 \times 0.5}{100} = ₹250$, not ₹3,000.

C · ₹6,000

$P = \frac{100 \times SI}{R \times T} = \frac{100 \times 480}{8 \times 1} = ₹6{,}000$.

B · The principal grows each year as interest is added to it

In simple interest the principal stays fixed; interest is never added to it. That is why each year's interest is identical — the other three statements are true.

D · ₹4,800

To find the total simple interest earned, we first calculate the interest for the first 4 years: \(SI_1 = \frac{15000 \times 12 \times 4}{100} = ₹7,200\). Then, for the next 2 years, the interest is: \(SI_2 = \frac{15000 \times 12 \times 2}{100} = ₹3,600\). The total interest is \(SI_1 + SI_2 = ₹7,200 + ₹3,600 = ₹10,80…