Suppose you have two bank accounts, one called Account A and another Account B. Account A will be worth $6,500.00 in one year. Account B will be worth $12,600.00 in two years. Both accounts earn 6% interest. What is the present value of each of these accounts?
Account A:
P = Po + Po*r*t = $6500.
Po + Po*0.06*1 = 6500.
Po + 0.06Po = 6500.
1.06Po = 6500.
Po = $6,132.08 = Present value.
Account B:
Same procedure as A.
To find the present value of each account, we need to discount the future values back to the present using the interest rate.
The formula to calculate the present value (PV) of an amount in the future is:
PV = FV / (1 + r)^n
Where:
PV = Present Value
FV = Future Value
r = Interest rate (expressed as a decimal)
n = Number of time periods
Let's calculate the present value for each account.
For Account A:
FV = $6,500.00
r = 6% = 0.06
n = 1 year
Using the formula:
PV = $6,500.00 / (1 + 0.06)^1
PV = $6,500.00 / 1.06
PV ≈ $6,132.08
The present value of Account A is approximately $6,132.08.
For Account B:
FV = $12,600.00
r = 6% = 0.06
n = 2 years
Using the formula:
PV = $12,600.00 / (1 + 0.06)^2
PV ≈ $12,600.00 / 1.1236
PV ≈ $11,216.93
The present value of Account B is approximately $11,216.93.
Therefore, the present value of Account A is approximately $6,132.08, and the present value of Account B is approximately $11,216.93.