Question

Calculate the amount and CI on ₹ 27,000 for `1 1/2` years at `6 2/3%` p.a., the interest being compounded semi-annually.

Answer 1

Given:

Principal P = 27,000

Rate of interest R = `6 2/3% = 6.6667%` per annum

Time T = 1.5 years

Compounding frequency: semi-annually 2 times per 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 semi-annual compounding, n = 2
• t is the time in years

Step 1: Calculate the amount and compound interest

Given:

• P = 27,000
• R = 6.6667%
• n = 2   ...(Compounded semi-annually)
• t = 1.5 years

The formula becomes `A = 27,000 (1 + (6.6667)/(100 xx 2))^(2 xx 1.5)`

Let me now calculate the amount and the CI.

The calculations are as follows:

• Amount (A) after `1 1/2` years at `6 2/3%` p.a., compounded semi-annually, is ₹ 29,791.01.
• Compound Interest (CI) is ₹ 2,791.01.