Which factor would be greater- the present value of $1 for 10 periods at 8% per period or the future value of $1 for 10 periods at 8% per period?
the present value of $1 for 10 periods at 8% per period
To determine which factor is greater, we need to calculate the present value and future value of $1 for 10 periods at 8% per period.
1. Present Value (PV) calculates the value of a future amount in today's dollars. It discounts future cash flows to their equivalent value in the present. The formula to calculate the present value is:
PV = FV / (1 + r)^n
Where:
- PV = Present Value
- FV = Future Value
- r = interest rate per period
- n = number of periods
In this case, we need to calculate the present value of $1 for 10 periods at 8% per period:
PV = 1 / (1 + 0.08)^10
2. Future Value (FV) calculates the value of an initial amount compounded over a specific period at a given interest rate. The formula to calculate the future value is:
FV = PV * (1 + r)^n
Where:
- FV = Future Value
- PV = Present Value
- r = interest rate per period
- n = number of periods
In this case, we need to calculate the future value of $1 for 10 periods at 8% per period:
FV = 1 * (1 + 0.08)^10
Now let's calculate both the present value and future value:
PV = 1 / (1 + 0.08)^10 ≈ 0.463
FV = 1 * (1 + 0.08)^10 ≈ 2.158
Therefore, the future value of $1 for 10 periods at 8% per period (2.158) is greater than the present value of $1 for 10 periods at 8% per period (0.463).