Question

A sum of Rs. 5,000 invested at 8% p.a., compounded semi-annually, amounts to

5,624.32. Calculate the time period of the investment​

Answer 1

Answer:

1.5 years

Step-by-step explanation:

A= P( 1+R/100)^2n

5624.32 = 5000(1+8/100)^2n

562432 / 500000 = (208 / 200)^2n

(26/25)^3 = (26/25)^2n

3=2n

n = 3/2 = 1.5 years

Answer 2

In 1.5 years ₹5000 will be ₹5624.32 at 8% interest compounded annually.

Given:

• A sum of Rs. 5,000 invested at 8% p.a., compounded semi-annually, amounts to 5,624.32.

To find:

• Calculate the time period of the investment.

Solution:

Formula to be used:

When interest compound semi-annually:

$\bf A = P \left( {1 + \frac{R}{200} } \right)^{2n}$

Here,

A: Total amount.

P: Principal amount

R: Rate of interest

n: Time period

Step 1:

Write the given values.

A: 5624.32

P: 5000

R: 8%

Step 2:

Find the time period.

Put the values in the formula.

$5624.32 = 5000 \left( {1 + \frac{8}{200} } \right)^{2n}$

$\frac{5624.32}{5000} = \left( { \frac{208}{200} } \right)^{2n}$

$\frac{562432}{500000} = \left( { \frac{208}{200} } \right)^{2n}$

$\left( \frac{26}{25} \right)^{3} = \left( \frac{26}{25} \right)^{2n}$

Compare the powers.

$2n = 3$

$n = \frac{3}{2}$

$\bf n = 1.5 \: years$

Thus,

In 1.5 years ₹5000 will be ₹5624.32 at 8% interest compounded annually.

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