Suppose your bank account will be worth $15,000.00 in one year. The interest rate (Discounted Rate) that the bank pays is 7%. What is the present value of your bank account today? What would the present value of the account be if the discount rate is only 4%?
To determine the present value of your bank account, you need to use the formula for calculating the present value of a future amount of money, which takes into account the interest rate and the time period.
The formula for calculating the present value (PV) is:
PV = FV / (1 + r)^n
Where:
PV = Present Value
FV = Future Value
r = Interest Rate
n = Time Period (in years)
Let's calculate the present value of your bank account, assuming an interest rate of 7% and a future value of $15,000.00:
PV = 15,000 / (1 + 0.07)^1
PV = 15,000 / 1.07
PV ≈ $14,018.69
Therefore, the present value of your bank account, assuming an interest rate of 7%, is approximately $14,018.69.
Now, let's calculate the present value of your bank account with a discount rate of 4%. We'll use the same future value of $15,000.00:
PV = 15,000 / (1 + 0.04)^1
PV = 15,000 / 1.04
PV ≈ $14,423.08
Therefore, the present value of your bank account, assuming an interest rate of 4%, is approximately $14,423.08.
By adjusting the interest rate, you can observe that the present value of the bank account decreases when the discount rate increases from 4% to 7%. This is because the higher the discount rate, the more the future value is discounted, leading to a lower present value.