Question

Many academic institutions offer a sabbatical policy. Every seventh year a professor is given a year free of teaching and other administrative responsibilities at full pay. For a professor earning $70,000 per year who works for a total of 42​ years, what is the present value of the amount she will earn while on sabbatical if the interest rate is 6% ​(EAR)? Note: Assume that the sabbatical annual salary is paid in one lump sum every 7 years.

Answer 1

The present value of the amount a professor will earn while on sabbatical is $266,996.60.

Step-by-step explanation:

To calculate the present value of the amount a professor will earn while on sabbatical, we can use the formula for present value of a future sum of money. The formula is:

PV = FV / (1 + r)^n

Where PV is the present value, FV is the future value, r is the interest rate, and n is the number of years.

In this case, the professor earns $70,000 per year and will work for 42 years. The sabbatical salary is paid in one lump sum every 7 years. So, the number of payments is 42 / 7 = 6.

Using the formula, the future value of the sabbatical salary is $70,000 * 6 = $420,000. The interest rate is 6% (EAR), so r = 0.06. And the number of years is 6.

Substituting the values into the formula, we have:

PV = $420,000 / (1 + 0.06)₆ = $266,996.60

Therefore, the present value of the amount the professor will earn while on sabbatical is $266,996.60.

Answer 2

$1,26,964.34

Step-by-step explanation:

As per the given question the solution of present value is provided below:-

To find out the present value first we need to calculate the interest rate

Interest rate 6%

Number of Years 7

Employment years 42

Number of sabbaticals 6 NPER

(7 year - 1 year)

Interest rate periodic 0.503630259 RATE (=1.06^7-1)

Salary 70000 PMT

Present value $1,26,964.34 =PV(rate,nper,Pmt)

To reach at present value we simply put the values into formula.

For more clarification please find the screenshot as attached.