The interest rate of a lump sum is the amount of interest received or paid on the lump sum, as the proportion of the amount deposited, lent or borrowed.

The present value, future value, frequency of compounding, and number of years over which the money is to be compounded are the four variables that determine the interest rate earned or paid on a lump sum.

## Steps to Calculating Interest rate of a lump sum

1. Determine the lump sum's future value, present value, frequency of compounding, and number of periods

2. Write the formula for calculating the interest rate of lump sum, which is as follow:

$$r=m\left(\frac{FV}{PV}\right)^{\frac{1}{n×m}}-m$$

3. Insert the value of the future value, present value, compound frequency, and number of periods of the lump sum into the formula.

4. Solve, solve and solve.

## Example

What should be the annual compound interest rate to make a lump sum of €30,000 to grow to €47,205 after 4 years given that interest is compounded yearly?

**Solution**

### Step 1: Determine the lump sum's future value, present value, frequency of compounding, and number of periods.

The future value of the lump sum is 47,205; its present value is 30,000; its compounding frequency is 1 because interest is compounded yearly.

### Step 2: Write the formula for calculating the interest rate of lump sum.

The formula for calculating interest rate of a lump sum is as follow:

$$r=m\left(\frac{FV}{PV}\right)^{\frac{1}{n×m}}-m$$

### Step 3: Insert the value of the future value, present value, compound frequency, and number of periods of the lump sum into the formula.

$r=1\left(\frac{47205}{30000}\right)^{\frac{1}{4×1}}-1$

### Step 4: Solve, solve and solve.

$r=\left(\frac{47205}{30000}\right)^{\frac{1}{4}}-1$

$r=1.5735^{\frac{1}{4}}-1$

$r=1.12-1$

$r=0.12$

Expressed in percentage

$r=12.00%

Therefore, the annual interest rate required to make a lump sum 30,000 to accumulate to 47,205 after 4 years is 12% per annum.

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