The financier is charging simple interest but is compounding it semi-annually. This means that the interest is added to the principal every six months and then interest is calculated on this new amount.

The nominal interest rate (the stated rate) is 10% per annum. But since it is compounded semi-annually, we need to calculate the effective annual rate (EAR) or the annual equivalent rate (AER), which is the actual interest earned or paid in a year.

Here are the steps to calculate the effective rate of interest:

1. Divide the annual nominal rate by the number of compounding periods in a year. In this case, it's 10% or 0.10 divided by 2 (since interest is compounded semi-annually), which equals 0.05 or 5%.

2. Add 1 to this rate. So, 1 + 0.05 = 1.05.

3. Raise the result to the power of the number of compounding periods. So, (1.05)^2 = 1.1025.

4. Subtract 1 from this result to get the effective interest rate. So, 1.1025 - 1 = 0.1025 or 10.25%.

So, the effective rate of interest becomes 10.25%.

Question

The financier is charging simple interest but is compounding it semi-annually. This means that the interest is added to the principal every six months and then interest is calculated on this new amount.

The nominal interest rate (the stated rate) is 10% per annum. But since it is compounded semi-annually, we need to calculate the effective annual rate (EAR) or the annual equivalent rate (AER), which is the actual interest earned or paid in a year.

Here are the steps to calculate the effective rate of interest:

1. Divide the annual nominal rate by the number of compounding periods in a year. In this case, it's 10% or 0.10 divided by 2 (since interest is compounded semi-annually), which equals 0.05 or 5%.

2. Add 1 to this rate. So, 1 + 0.05 = 1.05.

3. Raise the result to the power of the number of compounding periods. So, (1.05)^2 = 1.1025.

4. Subtract 1 from this result to get the effective interest rate. So, 1.1025 - 1 = 0.1025 or 10.25%.

So, the effective rate of interest becomes 10.25%.

Knowee AI · Accepted Answer

The financier is charging simple interest but is compounding it semi-annually. This means that the interest is added to the principal every six months and then interest is calculated on this new amount.

The nominal interest rate (the stated rate) is 10% per annum. But since it is compounded semi-annually, we need to calculate the effective annual rate (EAR) or the annual equivalent rate (AER), which is the actual interest earned or paid in a year.

Here are the steps to calculate the effective rate of interest:

1. Divide the annual nominal rate by the number of compounding periods in a year. In this case, it's 10% or 0.10 divided by 2 (since interest is compounded semi-annually), which equals 0.05 or 5%.

2. Add 1 to this rate. So, 1 + 0.05 = 1.05.

3. Raise the result to the power of the number of compounding periods. So, (1.05)^2 = 1.1025.

4. Subtract 1 from this result to get the effective interest rate. So, 1.1025 - 1 = 0.1025 or 10.25%.

So, the effective rate of interest becomes 10.25%.

An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:

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