Final answer:
The future value of $700 compounded at 5% for 10 years is $1,140.22, and at 10% it is $1,815.62. The present value of $700 due in 10 years at 5% is $429.89. For $2,160 due in 10 years, the present value at 10% is $833.11, and at 5% is $1,326.95. The present value is today's value of a future sum of money.
Step-by-step explanation:
Compound Interest and Present Value Calculations
To calculate the future value of an initial investment compounded annually, we use the formula FV = PV(1 + r)^n, where FV is the future value, PV is the present value or initial amount, r is the annual interest rate (as a decimal), and n is the number of years.
a. An initial $700 compounded for 10 years at 5% would be calculated as follows: FV = $700(1 + 0.05)^{10} = $700(1.62889) ≈ $1,140.22.
b. An initial $700 compounded for 10 years at 10% is calculated as: FV = $700(1 + 0.10)^{10} = $700(2.59374) ≈ $1,815.62.
To calculate present value, we use the formula PV = FV / (1 + r)^n.
c. The present value of $700 due in 10 years at 5% is calculated as: PV = $700 / (1 + 0.05)^{10} = $700 / 1.62889 ≈ $429.89.
d. To find the present value of $2,160 due in 10 years at both 10% and 5%:
- Present value at 10%: PV = $2,160 / (1 + 0.10)^{10} = $2,160 / 2.59374 ≈ $833.11.
- Present value at 5%: PV = $2,160 / (1 + 0.05)^{10} = $2,160 / 1.62889 ≈ $1,326.95.
e. The definition of present value is:
i. The present value is the value today of a sum of money to be received in the future and in general is less than the future value. This is the correct definition, as the present value reflects the current worth of a future amount, considering the time value of money and interest rates.