Question

Find the CI on ₹ 64000 for `1 1/2` years at 5% p.a., the interest being compounded half-yearly.

Answer 1

Given:

• Principal P = 64,000
• Rate of interest R = 5% per annum
• Time T = 1.5 years
• Compounding frequency: half-yearly (2 times a year)

Formula for Compound Interest (CI) when compounded n times a year:

`A = P(1 + R/(100n))^(nt)`

Where: 

•  A is the amount after time t
• P is the principal
• R is the rate of interest per annum
• n is the number of times interest is compounded per year (for half-yearly compounding, n = 2)
• t is the time in years

Step 1: Calculate the amount A

A = `64000 (1 + 5/(100xx2))^(2 xx 1.5)` 

A = `64000 (1 + 5/200)^3`

A = 64000 (1 + 0.025)³

A = 64000 × (1.025)³

A = 64000 × 1.076890625

A = 68800.625

Step 2: Calculate the compound interest (CI)

CI = A− P

CI = 68800.625 − 64000

CI = 4800.625