Question

A sum of money if invested at compound interest for 2 years amounts to ₹ 57,600 and ₹ 65,536 in 4 years. Find the rate and the sum.

Answer 1

Given:

• Amount after 2 years = ₹ 57,600
• Amount after 4 years = ₹ 65,536
• We are to find:
  • The rate of compound interest   ...(Per annum)
  • The original principal   ...(Sum)

Step 1: Use compound interest formula

We know:

`"Amount"_("4 years") = "Amount"_("2 years") xx (1 + r/100)^2`

Because:

`A_4 = A_2 xx (1 + r/100)^2`

Substitute values:

`65,536 = 57,600 xx (1 + r/100)^2`

`(1 + r/100)^2 = (65,536)/(57,600)`

`(1 + r/100)^2 = 1.1375`

Take square root of both sides:

`1 + r/100 = sqrt(1.1375)`

`1 + r/100 = 1.0667`

`r/100 = 1.0667 - 1`

`r /100 = 0.0667`

⇒ r = 6.67%

 ⇒ `r = 6 2/3%` 

Step 2: Find the Principal (sum)

We now use the CI formula:

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

Use:

• A = ₹ 57,600
• `r = 6 2/3% = 20/3`
• n = 2

So:

`57,600 = P(1 + 20/300)^2`

= `P(16/15)^2`

= `P xx 256/225`

`P = (57,600 xx 225)/256`

= `(12,960,000)/256`

= ₹ 50,625