Question

An athlete signs a contract that guarantees a ​$ 9​-million salary 6 yr from now. Assuming that money can be invested at 6.7​% with interest compounded​ continuously, what is the present value of that​ year's salary?

Answer 1

To calculate the present value of a future salary, we can use the formula for continuous compound interest. Plugging in the values given, the present value of the salary is approximately $5,767,555.13.

Step-by-step explanation:

To calculate the present value of a future salary, we need to use the formula for continuous compound interest:

PV = FV / (e(rt))

where:

• PV is the present value
• FV is the future value
• e is the base of the natural logarithm (approximately 2.71828)
• r is the interest rate
• t is the number of years

In this case, the future value is $9 million, the interest rate is 6.7%, and the number of years is 6. Plugging these values into the formula:

PV = 9,000,000 / (e(0.067*6))

Using a calculator, the present value of the salary is approximately $5,767,555.13.

Answer 2

$6,020,826.711

Step-by-step explanation:

The computation of the present value of that year salary is shown below:

As we know that

Present value in case of continuous compounding, the formula is

`= (Guaranteed\ amount)/(e^(0.067 * 6))`

where,

The Guaranteed amount is $9,000,000

The Time period is 6 years

And, the interest rate is 6.7%

Now placing these values

So, the present value is

`= (\$9,000,000)/(e^(0.067 * 6))`

= $6,020,826.711