Aman took a loan of ` 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after 1 1 2 years, if the interest is compounded: a) Annually b) Half yearly.
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The compound interest formulae when it is compounded :
1. Annually
(1 + i)ⁿ
Where i is the interest rate and n the period in years.
80000 × (1.1)¹¹²
80000 × 43249.46 = 3.4599568 × 10⁹
2. Half yearly
(1 + i/2)²ⁿ
10/2 = 5%
2 × 112 = 224
80000 × (1.05)²²⁴ =
80000 × 55770 = 4.461624 × 10⁹
THE DIFFERENCE
4.461624 × 10⁹ — 3.4599568 × 10⁹ = 1.0016672 × 10⁹
1. Annually
(1 + i)ⁿ
Where i is the interest rate and n the period in years.
80000 × (1.1)¹¹²
80000 × 43249.46 = 3.4599568 × 10⁹
2. Half yearly
(1 + i/2)²ⁿ
10/2 = 5%
2 × 112 = 224
80000 × (1.05)²²⁴ =
80000 × 55770 = 4.461624 × 10⁹
THE DIFFERENCE
4.461624 × 10⁹ — 3.4599568 × 10⁹ = 1.0016672 × 10⁹
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