Question

In what time will ₹64000 amount to ₹68921 at 5% per annum interest being compounded half yearly?

Answer 1

In 1½ Years interest being compounded half yearly.

Given:

• Principal = 64000
• Amount = ₹ 68921
• Rate = 5%

Explanation:

Suppose the Time be x

FORMULA

$\circ {\boxed{\underline{\sf{ Amount = P \left( 1 + \dfrac{r}{100} \right)^n }}}}$

Where as:

• P = Principal
• r = Rate
• n = Time

According to Question,

$\\ \colon\implies{\sf{ 68921 = 64000 \left( 1 + \dfrac{5}{100} \right)^x }} \\ \\ \\ \colon\implies{\sf{ 68921 = 64000 \left( \cancel{ \dfrac{105}{100} } \right) ^x }} \\ \\ \\ \colon\implies{\sf{68921 = 64000 \left( \dfrac{21}{20} \right) ^x }} \\ \\ \\ \colon\implies{\sf{ 68921 = \cancel{6400} \times \dfrac{21x}{ \cancel{20} } }} \\ \\ \\ \colon\implies{\sf{ 68921 = 3200 \times 21x }} \\ \\ \\ \colon\implies{\sf{ \dfrac{68921}{ 3200 \times 21 } = x }} \\ \\ \\ \colon\implies{\boxed{\mathfrak\pink{ x = 1 \dfrac{1}{2} }}}$

Hence,

• Time taken will be 1½ Years .