A bank offers 7.8% compound interest per annum calculated on a half-yearly basis. A customer deposits ₹9,920 each on 1 January and 1 July of a year. At the end of the year, the amount he would have gained by way of interest is ______ (give your answer correct to 2 decimal places).​

Correct option is A

Given:

Compound Interest rate = 7.8% per annum (half-yearly basis)

Amount deposited = ₹9,920 on 1 Jan and ₹9,920 on 1 July

Concept Used:

CI is calculated using the formula: A =  $$P(1 + r)^n$$​​

For half-yearly compounding, r = annual rate / 2, and n = number of half-years

Solution:

Rate per half-year = 7.8 / 2 = 3.9% = 0.039

Amount A1 = $$9920 × (1 + 0.039)^2$$​​

Amount A2 = 9920 × (1 + 0.039)

A1 = $$₹9920 × (1.039)^2 ≈ ₹10708.84$$8​

A2 = ₹9920 × 1.039 ≈ ₹10306.88

Total amount = ₹10708.848 + ₹10306.88 = ₹21015.728

Total principal = ₹19840

Compound Interest = ₹21015.728 - ₹19840 = ₹1175.73

₹1175.73