Simple & compound interest: Quantitative Aptitude Notes for Andaman & Nicobar Islands Forest Guard

Simple & Compound Interest – Forest Guard Study Notes

(Quantitative Aptitude – Andaman & Nicobar Islands Forest Guard)

Term	What it means	How it’s computed
Principal (P)	Original amount of money lent or invested	Input value
Rate of Interest (r)	Annual rate expressed in %	Given or to be found
Time (t)	Number of years	Given or to be found
Simple Interest (SI)	Interest earned only on the principal	`SI = P × r × t / 100`
Compound Interest (CI)	Interest earned on the principal and on previously earned interest	`CI = P × ( (1 + r/100)^t – 1 )`

Simple Interest: linear growth – one interest calculation per year.
Compound Interest: exponential growth – interest on interest each compounding period (yearly, half‑yearly, quarterly, monthly, daily, etc.).

Concept	Formula	Notes
Simple Interest	`SI = P × r × t / 100`	Rate & time must be in same units (years).
Total Amount (Simple)	`A = P + SI`	`A = P (1 + r t / 100)`
Compound Interest	`CI = P × ( (1 + r/100)^t – 1 )`	Compounding period = 1 year.
Total Amount (Compound)	`A = P × (1 + r/100)^t`	`A = P (1 + r/100)^t`
Compound with k‑times compounding per year	`A = P × (1 + r/(100k))^(k t)`	Example: quarterly → k = 4.
Interest Rate (r) from given A, P, t (simple)	`r = 100 × SI / (P t)`	Use `r = 100 (A – P) / (P t)`
Interest Rate (r) from given A, P, t (compound)	`r = 100 × ( (A/P)^(1/t) – 1 )`	Solve for `r` by algebraic manipulation.
Effective Annual Rate (EAR)	`EAR = (1 + r/100)^k – 1`	Where `k` = compounding frequency per year.
Rule of 72 (approx. doubling time)	Doubling time ≈ 72 / r	`r` in % per year.

A forest guard invests ₹50,000 in a bank for 3 years at an annual rate of 8 %.

Question a: How much simple interest will he earn?
Question b: How much total amount will he receive if the interest is compounded quarterly?

Step‑by‑step

Identify:
- (P = ₹50,000)
- (r = 8%)
- (t = 3) years
Apply formula:
[ SI = \frac{P \times r \times t}{100} = \frac{50,000 \times 8 \times 3}{100} = \frac{1,200,000}{100} = ₹12,000 ]
Total amount:
[ A = P + SI = 50,000 + 12,000 = ₹62,000 ]

Answer: Simple interest earned = ₹12,000; total amount = ₹62,000.

Step‑by‑step

Identify:
- (P = ₹50,000)
- Annual rate (r = 8%)
- Time (t = 3) years
- Compounding frequency (k = 4) (quarterly)
Compute periodic rate:
[ \text{Periodic rate} = \frac{r}{100k} = \frac{8}{100 \times 4} = 0.02 = 2% ]
Apply compound formula:
[ A = P \left(1 + \frac{r}{100k}\right)^{k t} = 50,000 \left(1 + 0.02\right)^{4 \times 3} = 50,000 \left(1.02\right)^{12} ]
Calculate (1.02^{12}):
- (1.02^{12} \approx 1.26824) (use calculator or exponent table)
Total amount:
[ A \approx 50,000 \times 1.26824 = ₹63,412 ]
Compound interest earned:
[ CI = A - P = 63,412 - 50,000 = ₹13,412 ]

Answer: Compounded quarterly, he will receive approximately ₹63,412 after 3 years, earning about ₹13,412 in interest.

Item	Formula	Quick Tips
Simple Interest	`SI = P r t / 100`	Think “only on principal”.
Total (Simple)	`A = P (1 + r t / 100)`	Same as `P + SI`.
Compound Interest	`CI = P ( (1 + r/100)^t – 1 )`	“Interest on interest”.
Total (Compound)	`A = P (1 + r/100)^t`	Use power directly.
k‑times compounding	`A = P (1 + r/(100k))^(k t)`	k = 1 (annual), 2 (half‑yearly), 4 (quarterly), 12 (monthly).
**Sol