Final answer:
To determine the better deal between paying $17,000 now or $4000 annually over 5 years with 6% interest, we need to calculate the present value for the different payment schedules. The best deal is the option with the lowest present value.
Step-by-step explanation:
Should you pay $17,000 today for new office computers or should you pay $4000 a year for 5 years (6% yearly interest rate)? To decide which is the better deal, we need to calculate the present value (PV) for both options. The present value helps us compare the value of money now versus money paid in the future.
a. Calculate the PV if you make payments at the beginning of the periods: When payments are made at the beginning of each period, they are considered annuities due. The formula for PV of an annuity due differs slightly because each payment is compounded one less time than in an ordinary annuity.
b. Calculate the PV if you make payments at the end of the periods: This scenario represents an ordinary annuity, where payments are made at the end of each period. To find the present value, we would use the formula for an ordinary annuity.
c. Calculate the PV if you make an extra payment of $750 at the end of the 5th year: In this case, we calculate the PV of the annuity (with the $4000 payments) first and then calculate the present value of the single $750 payment at the end of the 5th year. The two figures are then added together to get the total present value.
d. What is the best deal? After calculating the present values for each scenario, the best deal is the option with the lowest present value, since it represents the least expensive option in today's dollars.