Question

Calculate compound interest on 1000 over a period of 1 year at 10% per annum, if
interest is compounded quarterly?
please answer in step by step way​

Answer 1

Step-by-step explanation:

Given

$principal(p) \: = 1000 \\ \\ rate(r) =1 0\% = \frac{10}{4} = 2.5 \: quartaly \\ \\ time(n) = 1 \: year \: = 4 \: quarerly$

• For a quarterly period multiply time by 4
• and divide rate by 4

$Amount\: = p(1 - \frac{r\%}{100} ) {}^{4} \\ \\ = 1000(1 + \frac{2.5}{100} ) {}^{4} \\ \\ = 1000(1 + \frac{1}{40} ) {}^{4} \\ \\ =1000 \times ( \frac{41}{40} ) {}^{4} \\ \\ = 1000 \times \frac{41}{40} \times \frac{41}{40} \times \frac{41}{40} \times \frac{41}{40} \\ \\ = \frac{41 \times 41 \times 41 \times 41}{2560} \\ \\ = \frac{2825761}{2560} \\ \\ = 1103.81$

Compound interest = 1103.81 - 1000

=₹ 103. 81