Question

2. Find the compound interest for the given principal, rate and time when compounded half-yearly.

P = 10,000, R = 6% p.a., T = 18 months ​

Answer 1

Given :

• Principal = Rs.10,000
• Rate = 6% p.a.
• Time = 18 months = 1½ years.

To Find :

The compound interest.

Solution :

Analysis :

Here we have to find the compound interest which is compounded half yearly that is half of rate and years.

Required Formula :

Compound Interest = [P(1 + R/100)ⁿ] - P

where,

• P = Principal
• R = Rate
• n = Time

Explanation :

It is said that the interest is compounded half yearly.

So,

• Rate = 6% = 6/2 = 3% p.a.

Since it is given that time is 1 ½ years that is 18 months. So for compounding half yearly, the time period will be 3 Half Years. Time = 2 × 3/2 = 3 half years.

We know that if we are given the principal, rate, time and is asked to find the compound interest then our required formula is,

Compound Interest = [P(1 + R/100)ⁿ] - P

where,

• P = Rs.10,000
• R = 3%
• n = 3

Using the required formula and substituting the required values,

⇒ Compound Interest = [P(1 + R/100)ⁿ] - P

⇒ Compound Interest = [10000(1 + 3/100)³] - 10000

⇒ Compound Interest = [10000((100 + 3)/100)³] - 10000

⇒ Compound Interest = [10000(103/100)³] - 10000

⇒ Compound Interest = [10000(103/100 × 103/100 × 103/100)] - 10000

⇒ Compound Interest = [10000 × 103/100 × 103/100 × 103/100] - 10000

⇒ Compound Interest = [1 × 103/1 × 103/1 × 103/100] - 10000

⇒ Compound Interest = [1 × 103 × 103 × 103/100] - 10000

⇒ Compound Interest = [103 × 103 × 103/100] - 10000

⇒ Compound Interest = [1092727/100] - 10000

⇒ Compound Interest = [10927.27] - 10000

⇒ Compound Interest = 10927.27 - 10000

⇒ Compound Interest = 927.27

∴ Compound Interest = Rs.927.27.

Explore More :

• SI = (P × R × T)/100
• Interest = Amount - Principal
• P = SI × 100/R × T
• R = SI × 100/P × T
• T = SI × 100/R × P

where,

• P = Principal
• R = Rate
• T = Time