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.

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 = \frac{FV}{(1 + r)^n} $, 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: \[ PV = \frac{FV}{(1 + r)^n} \]

Step 3: Substitute the Values

Substituting the known values into the formula: \[ PV = \frac{47000}{(1 + 0.07)^1} \]

Step 4: Calculate the Present Value

Calculating the denominator: \[ 1 + 0.07 = 1.07 \] Now substituting back: \[ PV = \frac{47000}{1.07} \approx 43925.2336 \]

Final Answer

Thus, the amount of cash that must be invested today is approximately \$\boxed{43925.23}\$.

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