Question

A sum of £ 1640 is invested in a bank. The rate of interest is 4 . 5 % per annum. Calculate the simple interest gained in 9 months.

Answer 1

The simple interest gained in 9 months is approximately £55.35.

To calculate the simple interest gained in 9 months for a sum of £1640 invested at a rate of 4.5% per annum, we can follow these steps:

Step 1: Understand the Formula for Simple Interest

The formula for simple interest is given by:

`\[ \text{Simple Interest (SI)} = \text{Principal (P)} * \text{Rate (R)} * \text{Time (T)} \]`

Here:

- Principal (P) is the initial amount invested.

- Rate (R) is the annual interest rate.

- Time (T) is the time period for which the interest is calculated.

Step 2: Convert the Rate to a Decimal

The annual interest rate is given as 4.5%. We need to convert this percentage to a decimal for calculation:

`\[ R = 4.5\% = (4.5)/(100) \]`

Step 3: Adjust the Time Period

The time period for the interest calculation is 9 months. Since the rate given is per annum (yearly), we need to convert the time period into years:

`\[ T = \frac{\text{Time in months}}{12} = (9)/(12) \]`

Step 4: Plug in the Values

Now, we will substitute the values into the simple interest formula:

- P = £1640

- R = 4.5% = 0.045 (as a decimal)

- T = 9/12 years

`\[ \text{SI} = 1640 * 0.045 * (9)/(12) \]`

Step 5: Calculate the Simple Interest

Let's calculate the simple interest gained in 9 months.

The simple interest gained in 9 months on a sum of £1640 invested at a rate of 4.5% per annum is approximately £55.35.