ICSE Class 9 Maths Chapter 03 Compound Interest

3. Compound Interest

Points To Remember

1. Simple Interest (S.I.) = \[\frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100} = \frac{Prt}{100}\]

Where P = Principal, or sum. r = Rate of p.a. t = Time in years Amount (A) = P + S.I.

2. Compound Interest (C.I.)

\[A = P\left(1+\frac{r}{100}\right)^n\]

where A = Amount r = rate of p.a. n = Period in years / half-years / quarters / Compound Interest (C.I.) = A - P

\[or \quad P\left[\left(1+\frac{r}{100}\right)^n - 1\right]\]

Exercise 3-A

Q. 1. Find the amount and the compound interest on Rs. 2500 for 2 years at 11% per annum.

Sol. Principal (P) = Rs. 2500 Rate (r) = 11% Period = 2 years

\[\therefore \text{S.I. for the first year} = \frac{Prt}{100}\]

\[= \frac{2500 \times 11 \times 1}{100} = 275\]

Amount = Principal + Interest = Rs. 2500 + 275 = 2775

\[\therefore \text{Principal for second year} = \text{Rs. 2775}\]

\[\text{Interest for the second year} = \frac{2775 \times 11 \times 1}{100} = \frac{30525}{100} = \text{Rs. 305.25}\]

\[\therefore \text{Amount} = P + A = \text{Rs. 2775 + Rs. 305.25}\] = Rs. 3080.25

and compound interest for 2 years = Rs. 3080.25 - Rs. 2500 = Rs. 580.25 Ans.

2. Find the amount and the compound interest on Rs. 20000 for 3 years at 9% per annum.

Sol. Principal (P) = Rs. 20000 Rate (r) = 9% p.a. Period (t) = 3 years

\[\therefore \text{Interest for the first year} = \frac{Prt}{100}\]

\[= \text{Rs.} \frac{20000 \times 9 \times 1}{100}\] = Rs. 1800

\[\therefore \text{Amount after first year}\] = Rs. 20000 + 1800 = Rs. 21800

Principal for the second year = Rs. 21800

\[\text{Interest for the second year} = \frac{21800 \times 9 \times 1}{100}\] = Rs. 1962

\[\therefore \text{Amount after second year}\] = Rs. 21800 + Rs. 1962 = Rs. 23762

Principal for the third year = Rs. 23762

\[\text{Interest for the third year} = \frac{23762 \times 9}{100} = \text{Rs. 2138.58}\]

\[\therefore \text{Amount after third year}\] = Rs. 23762 + Rs. 2138.58 = Rs. 25900.58

and compound interest for 3 years = Rs. 25900.58 - Rs. 20000 = Rs. 5900.58 Ans.

3. Find the difference between simple interest and the compound interest on Rs. 9500 for 2 years at 8% per annum.

Sol. Principal (P) = Rs. 9500 Rate (r) = 8% p.a. Period (n) = 2 years

\[\therefore \text{Simple Interest} = \frac{Prn}{100}\]

\[= \text{Rs.} \frac{9500 \times 8 \times 2}{100}\] = Rs. 1520

\[\text{Interest for the first year} = \text{Rs.} \frac{9500 \times 8 \times 1}{100}\] = Rs. 760

\[\therefore \text{Amount after first year} = \text{Rs. 9500 + 760}\] = Rs. 10260

and principal for the second year = Rs. 10260

\[\text{Interest for the second year} = \frac{10260 \times 8 \times 1}{100}\] = Rs. 820.80

\[\therefore \text{Amount after second year}\] = Rs. 10260 + Rs. 820.00 = Rs. 11080.80

and compound interest = A - P = Rs. 11080.80 - 9500 = Rs. 1580.80

Difference between simple interest and compound interest = Rs. 1580.80 - Rs. 1520 = Rs. 60.80 Ans.

4. Kiran borrowed Rs. 18000 from her friend shaloo at 15% per annum simple interest lent it to Rahul at the same rate but compounded annually. Find her gain after 3 years.

Sol. Principal (P) = Rs. 18000 Rate (r) = 15% p.a.

period (x) = 3 years

\[\therefore \text{Simple interest by Kiran}\] \[= \frac{Prn}{100} = \frac{18000 \times 15 \times 3}{100}\] = Rs. 8100

When interest is compounded annually

\[\text{Interest for the first year} = \frac{18000 \times 15 \times 1}{100}\] = Rs. 2700

Amount after first year = Rs. 18000 + 2700 = Rs. 20700

\[\therefore \text{Principal for the second year} = \text{Rs. 20700}\]

\[\text{Interest for the second year} = \text{Rs.} \frac{20700 \times 15 \times 1}{100}\] = Rs. 3105

Amount after second year = Rs. 20700 + 3105 = Rs. 23805

\[\therefore \text{Principal for the third year} = \text{Rs. 23805}\]

\[\text{Interest for the third year} = \frac{23805 \times 15 \times 1}{100}\] = Rs. 3570.75

Amount after third year = Rs. 23805 + Rs. 3570.75 = Rs. 27375.75

Compound interest received by shaloo = Rs. 27375.75 - Rs. 18000 = Rs. 9375.75

\[\therefore \text{Her gain} = 9375.75 - 8100.00\] = Rs. 1275.75 Ans.

5. Deepak deposited a sum of Rs. 32500 in a bank for 1 year 1 compounded half-yearly at 12% per annum. Find the compound interest, he gets.

Sol. Principal (P) = Rs. 32500 Rate (r) = 12% p.a. or 6% half-yearly Period (n) = 1 year or 2 half-years

\[\text{Interest for the first half-year} = \frac{Prn}{100} = \frac{32500 \times 6 \times 1}{100}\] = Rs. 1950

Amount after one year = Rs. 32500 + 1950 = Rs. 34450

\[\therefore \text{Principal for the second half-year} = \text{Rs. 34450}\]

\[\text{Interest} = \frac{34450 \times 6 \times 1}{100}\] \[= \text{Rs.} \frac{206700}{100} = \text{Rs. 2067}\]

\[\therefore \text{Total interest for 2 half-years}\] = Rs. 1950 + 2067 = Rs. 4017 Ans.

6. Pulkit borrowed Rs. 16000 from a finance company at 15% per annum compounded half-yearl. What amount of money

discharge his debt after 1 \[\frac{1}{2}\] years?

Sol. Sum borrowed (P) = Rs. 16000

Rate (r) = 15% p.a. or \[\frac{15}{2}\]% half-yearly

Period (n) = 1\[\frac{1}{2}\] years or 3 half-years

\[\text{Interest for the first half-year} = \frac{Prn}{100}\]

\[= \frac{16000 \times 15 \times 1}{100 \times 2} = \text{Rs. 1200}\]

Amount after first half-year = Rs. 16000 + 1200 = Rs. 17200

Principal for the second half-year = Rs. 17200

\[\therefore \text{Interest for the second half-year}\]

\[= \text{Rs.} \frac{17200 \times 15 \times 1}{100 \times 2} = \text{Rs. 1290}\]

\[\therefore \text{Amount after second half-year}\] = Rs. 17200 + 1290 = Rs. 18490

Teacher's Note

Compound interest is used in real savings accounts and loans - when you save money in a bank, the interest earned each period is added to your balance, and the next period's interest is calculated on this larger amount, helping your savings grow faster.

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