Question

At what rate percent will a sum of ₹ 64,000 yield ₹ 4921 as CI in `1 1/2` years when compounded half yearly?

Answer 1

Step 1: Given

• Principal (P) = ₹ 64,000
• Compound Interest (CI) = ₹ 4,921
• Time = `1 1/2` years = 3 half-years (since compounding is half-yearly)

Step 2: Relation between Amount and Principal

A = P + CI

= 64000 + 4921

= ₹ 68,921

Formula:

`A = P(1 + r/200)^n`

where r = annual rate of interest,

And n = number of half-years = 3.

Step 3: Substitution

`68921 = 64000(1 + r/200)^3`

`68921/64000 = (1 + r/200)^3`

`1.076890625 = (1 + r/200)^3`

Step 4: Take cube root

`1 + r/200 = root(3)(1.076890625)`

`1 + r/200 ≈ 1.025`

`r/200 = 0.025`

⇒ r = 5

The required rate of interest is 5% per annum (compounded half-yearly).