Question

You've just joined the investment banking firm of dewey, cheatum, and howe. they've offered you two different salary arrangements. you can have $7,400 per month for the next two years, or you can have $6,100 per month for the next two years, along with a $33,000 signing bonus today. assume the interest rate is 6 percent compounded monthly. if you take the first option, $7,400 per month for two years, what is the present value? (do not round intermediate calculations and round your answer to 2 decimal places,

e.g., 32.16.) present value $ what is the present value of the second option? (do not round intermediate calculations and round your answer to 2 decimal places,
e.g., 32.16.) present value $

Answer 1

To calculate the present value of each salary option provided by the investment banking firm, use the present value of an annuity formula for the monthly payments and add any lump-sum payments received today without discounting. Keep intermediate calculations exact and round the final answers to two decimal places.

Step-by-step explanation:

The question asks to calculate the present value of two different salary arrangements under a 6% monthly compounded interest rate. To find the present value of the first option ($7,400 per month for two years), we use the present value of an annuity formula. Similarly, we calculate the present value of the second option ($6,100 per month for two years and a $33,000 signing bonus), by adding the present value of the monthly payments to the present value of the signing bonus.

For the first option:

• Monthly Payment (PMT): $7,400
• Number of Periods (n): 24 months (2 years)
• Monthly Interest Rate (i): 0.5% (since 6% annually compounded monthly)
• Present Value (PV) formula for an annuity: PV = PMT × [(1 - (1 + i)^-n) / i]

Applying this to the first option:

PV = $7,400 × [(1 - (1 + 0.005)^-24) / 0.005]

For the second option:

• Present value of the annuity (monthly payments): Calculate as above with PMT = $6,100
• Present value of the signing bonus: $33,000 (since it's received today, no discounting)
• Add the two present values to find the total present value of the second option.

Remember to keep intermediate calculations exact and round only the final result to two decimal places.

Answer 2

If you take the question very literally, you have just joined the organisation and been offered two options. The present value of each is still $0 as you have not yet selected either or received any payment. However, assuming the question is aimed at establishing which option is better over the two year period, the following explanation applies. Salary arrangement 1 is 7,400 monthly for 24 months Assuming the whole salary is invested each month, and the annual interest rate is 6%, and that it is paid at the start of each month then the following formula will apply: Present value = previous value + (previous value * interest rate) + monthly payment Using this formula for a 24 month period results in present value of $188,196.47 Salary arrangement 2 is 33,000 initially and 6,100 monthly for 24 months Using the same assumptions as above, and the same formula for 24 month period results in present value of $191,692.01 The main difference is the initial payment which is accruing interest throughout the period and therefore salary arrangement 2 results in a higher present value.