If the interest rate is 3% and a total of $4,370.91 will be paid to you at the end of 3 year, what is the present value of that sum.
We do not know if it is simple or compound interest. Since compounding frequency is not mentioned, we assume it is simple interest.
The simple interest formula:
Future value = present value(1+ni)
n=number of years,
i=annual interest
So
4,370.91 =PV(1+3*0.03)
=>
PV=4,370.91/(1.09)
=$4010
To find the present value of a future sum, we can use the formula for calculating the present value of a single amount:
Present Value = Future Value / (1 + Interest Rate)^n
Where:
- Future Value is the amount to be received in the future
- Interest Rate is expressed as a decimal (e.g., 3% = 0.03)
- n is the number of periods (in this case, 3 years)
Let's plug in the values and calculate the present value:
Present Value = $4,370.91 / (1 + 0.03)^3
Calculating the denominator:
(1 + 0.03)^3 = (1.03)^3 = 1.092727
Now, substitute the denominator value into the formula:
Present Value = $4,370.91 / 1.092727
Calculating the division:
Present Value ≈ $3,999.99 (rounded to two decimal places)
Therefore, the present value of $4,370.91 to be received at the end of 3 years with an interest rate of 3% is approximately $3,999.99.
To calculate the present value of a future sum, you need to use the present value formula. The formula is as follows:
Present Value = Future Value / (1 + Interest Rate) ^ Number of Periods
In this case, we have the following information:
Future Value = $4,370.91 (the sum that will be paid to you at the end of 3 years)
Interest Rate = 3% (or 0.03 as a decimal)
Number of Periods = 3 years
Now, let's plug in these values into the formula and calculate the present value.
Present Value = $4,370.91 / (1 + 0.03) ^ 3
Calculating the equation inside the parentheses first: (1 + 0.03) ^ 3 results in (1.03) ^ 3 = 1.092727.
Now, substituting this value back into the formula:
Present Value = $4,370.91 / 1.092727
Finally, let's solve this division:
Present Value ≈ $4,000.00
Therefore, the present value of $4,370.91 to be received at the end of 3 years, with an interest rate of 3%, is approximately $4,000.00.