Questions: What amount of cash must be invested today in order to have 47,000 at the end of one year, assuming the rate of return is 7% (PV of 1 and PVA of 1) Note: Use appropriate factor(s) from the tables provided.
Transcript text: What amount of cash must be invested today in order to have $\$ 47,000$ at the end of one year, assuming the rate of return is $7 \%$ (PV of $\$ 1$ and PVA of \$1)
Note: Use oppropriate factor(s) from the tables provided.
Solution
Solution Steps
To find the present value (PV) of a future amount, we use the formula for the present value of a single sum: PV=(1+r)nFV, where FV is the future value, r is the rate of return, and n is the number of periods. In this case, FV=47,000, r=0.07, and n=1.
Step 1: Identify the Variables
We are given the future value FV=47000, the rate of return r=0.07, and the number of periods n=1.
Step 2: Apply the Present Value Formula
To find the present value PV, we use the formula:
PV=(1+r)nFV
Step 3: Substitute the Values
Substituting the known values into the formula:
PV=(1+0.07)147000
Step 4: Calculate the Present Value
Calculating the denominator:
1+0.07=1.07
Now substituting back:
PV=1.0747000≈43925.2336
Final Answer
Thus, the amount of cash that must be invested today is approximately \\(\boxed{43925.23}\\).