Suppose you want to have $5,000 saved at the end of five years. The bank will pay 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 calculate how much you would need to deposit today to have $5,000 at the end of five years with a 2% interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment (in this case, $5,000)
P = the principal amount (the initial deposit we need to find)
r = the annual interest rate (2% in this case)
n = the number of times that interest is compounded per year (this information is not provided, so we'll assume it's compounded annually)
t = the number of years (5 in this case)
Let's plug in the given values into the formula and solve for P:
$5,000 = P(1 + 0.02/1)^(1*5)
Simplifying further:
$5,000 = P(1.02)^5
To isolate P, divide both sides by (1.02)^5:
P = $5,000 / (1.02)^5
Calculating this using a calculator or spreadsheet software, we find that P is approximately $4,415.40.
Therefore, you would need to deposit approximately $4,415.40 today to have $5,000 at the end of five years with a 2% interest rate.