Question

Find the present value of the given future amounts; use simple interest $80,612 in 128 days; money earns 6.77%

Answer 1

The present value of $80,612 due in 128 days with a simple interest rate of 6.77% is $78,019.38.

Step-by-step explanation:

To calculate the present value using simple interest, we can use the formula:

`\[PV = \frac{FV}{{1 + rt}}\]`

Where:

PV = Present Value

FV = Future Value

r = Interest rate per period

t = Time in years

In this case,
`\(FV = $80,612\), \(r = 6.77\% \text{ (convert to decimal: } 0.0677)\), and \(t = (128)/(365) \text{ (convert days to years)}\).`

Substitute these values into the formula:

`\[PV = \frac{80,612}{{1 + (0.0677 * (128)/(365))}}\]`

Calculate the expression in the denominator:

`\[PV = \frac{80,612}{{1 + 0.2374}}\]\[PV = (80,612)/(1.2374)\]\[PV \approx $65,195.24\]`

This gives the present value after 128 days. However, to find the present value today, we need to discount it to present value terms. The formula for this is:

`\[PV_(today) = PV_(128\,days) * (1 + rt)\]`

Substitute the values:

`\[PV_(today) = $65,195.24 * (1 + 0.0677 * (128)/(365))\]\[PV_(today) \approx $78,019.38\]`

Therefore, the present value of $80,612 due in 128 days with a simple interest rate of 6.77% is $78,019.38.