Math 10

Compound Interest

? The amount in T year = P (1 + R%)T = P 1+ R T
100
R R T–
Also, the interest in T year = P 1+ 100 T–P =P 1 + 100 1

Thus,

Compound amount = P 1+ R T and Compound interest = P 1 + R T– 1
100 100

1. When the interest is compounded annually but the rate being different in different

years, for example, R1% in the first year, R2% in the second year, R3% in the third
years, then the amount in 3 years is calculated as,

Compound Amount =P 1 + R1 1 + R2 1 + R3
100 100 100

Also, Compound Interest = P 1 + R1 1 + R2 1 + R3 –1
100 100 100

2. When the interest is compounded annually but the time is given in 'T' years and 'M'
months, then the amount is calculated as

Compound Amount =P 1 + R T 1 + MR
100 1200

Also, Compound Interest = P 1 + R T 1 + MR –1
100 1200

3.3 Interest compounded half-yearly and quarter-yearly
R
If the compound interest is payable half yearly, then rate = 2 % per half yearly and

time = 2T half years. R 2T
× 100
Now, the compound amount half yearly= P 1 + 2

Also, the compound interest half yearly = P 1 + 2 R 2T – 1
× 100

Similarly, if the compound interest is payable quarter-yearly (every 3 months),

then rate = R % per quarter-yearly and time = 4T quarter years.
4

So, the compound amount quarter-yearly =P 1 + R 4T
× 100
4

And the compound interest quarter-yearly = P 1 + 4 R 4T – 1
× 100

Worked-out examples

Example 1: Calculate the compound interest of Rs 7,000 at 10% per annum for 3 years

without using the formula.

Solution:

Here, principal (P) = Rs 7,000

Rate of interest (R) = 10% p.a.

Now, Time (T) = 3 years = PTR = 7,000 × 1 × 10
the interest in the first year (I1) 100 100

= Rs 700

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 49 Vedanta Excel in Mathematics - Book 10

Compound Interest

? The principal for the second year = Rs 7,000 + Rs 700
Now, the interest in the second year (I2)
= Rs 7,700

= 7,700 × 1 × 10
100
= Rs 770

? The principal for the third year = Rs 7,700 + Rs 770
Again, the interest in the third year (I3)
= Rs 8,470

= 8,470 × 1 × 10
100
= Rs 847

? The compound interest (C.I.) = I1 + I2 + I3

= Rs 700 + Rs 770 + Rs 847 = Rs 2,317

Example 2: A sum of Rs 24,000 is deposited in a bank X at the rate of 5% p.a. simple
interest. If the sum would have been deposited in bank Y at the same rate of
compound interest, which bank would give more interest after 3 years and
by how much?

Solution:

Here, principal (P) = Rs 24,000, time (T) = 3 years and rate (R) = 5 % p.a.

Now, simple interest = PTR = Rs 24,000 × 3 × 5 = Rs 3,600
100 100
R
Also, compound interest = P 1 + 100 T– 1

= Rs 24,000 1 + 5 3 –1
100

= Rs 24,000 1 + 1 3– 1
20

= Rs 24,000 21 3 – 1
20

= Rs 24,000 21 × 21 × 21 – 8,000 = Rs 3 × 1261 = Rs 3,783
8,000

? Difference of compound and simple interest = Rs 3,783 – Rs 3,600 = Rs 183

Hence, bank Y would give more interest by Rs 183.

Example 3: Laxmi deposited Rs 16,000 at 10% p.a. interest compounded semi-annually
cfoorm1p12ouyenadresd.
Narayan deposited the equal sum at the same rate of interest
annually for the same duration of time. Who gets more interest

and by how much?

Solution:
Here, principal (P) = Rs 16,000, time (T) = 112 years and rate (R) = 10 % p.a.
R
Now, interest compounded semi annually (I1) = P 1 + 2 ×100 2T– 1

= Rs 16,000 1 + 10 3– 1
200
21 × 21 × 21
= Rs 16,000 20 × 20 × 20 –1

= Rs 2,522

Vedanta Excel in Mathematics - Book 10 50 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur