Question

If principal = Rs 1,00,000. rate of interest = 10% compounded half yearly. Find

1. Interest for 6 months.
2. Amount after 6 months.
3. Interest for next 6 months.
4. Amount after one year.

Answer 1

Principal (P) = ₹ 100000

Rate of interest (R) = 10% compounded half-yearly

i. Interest for 6 months,

We know that,

Compound interest, CI = A – P

Where, ${\displaystyle A=P{(1+\frac{R}{200})}^n}$  ...[For 6 months]

∴ ${\displaystyle A=P{(1+\frac{R}{200})}^n=100000{(1+\frac{10}{200})}^1}$  ...[∵ n = 1 for 6 months]

= ${\displaystyle 100000\times \frac{21}{20}}$

= ₹ 105000

∴ Compound interest, CI = A – P

= ₹ 105000 – ₹ 100000

= ₹ 5000

ii. Amount after 6 months = ₹ 105000

iii. Interest for next 6 months

Principal = Amount after 6 months

∴ Principal (P) = ₹ 105000

Rate of interest (R) = 10%

∴ ${\displaystyle A=P{(1+\frac{R}{200})}^n}$

= ${\displaystyle 105000{(1+\frac{10}{200})}^1}$  ...[∵  n = 1 for 6 months]

= ${\displaystyle 105000\times \frac{21}{20}}$

= ${\displaystyle \frac{2205000}{20}}$

= ₹ 110250

∵ Compound interest, CI = A – P

= ₹ 110250 – ₹ 105000

= ₹ 5250

iv. Amount after one year = ₹ 110250