Suppose you want to have $5,000 saved at the end of five years. The bank will pay you 2% interest on your money. How much would you have to deposit today to have the $5,000 you want at the end of five years.
To determine how much you would need to deposit today in order to have $5,000 at the end of five years with a 2% interest rate, you can use the formula for calculating the future value of an investment, known as the compound interest formula. The formula is:
FV = PV * (1 + r)^n
Where:
FV = Future value of the investment
PV = Present value or the initial deposit
r = Interest rate per period (expressed as a decimal)
n = Number of periods
In this case, you want to calculate the present value (PV) of the investment. Rearranging the formula, we have:
PV = FV / (1 + r)^n
Let's apply these values to the formula:
FV = $5,000
r = 2% = 0.02 (expressed as a decimal)
n = 5 years
Now, substitute these values into the formula:
PV = $5,000 / (1 + 0.02)^5
Next, let's simplify the expression inside the parentheses:
(1 + 0.02)^5 = (1.02)^5
Calculating this value, we find:
(1.02)^5 = 1.10408
Now, substitute this value into the formula:
PV = $5,000 / 1.10408
Finally, solving for PV:
PV ≈ $4,524.33
Therefore, you would need to deposit approximately $4,524.33 today in order to have $5,000 at the end of five years with a 2% interest rate.