Question

Assuming that you are a hospital administrator and you realize that a major piece of medical equipment needs to be replaced in four (4) years time, determine how much money needs to be set aside from the hospital's monthly revenues for the next 48 months in order to pay for the anticipated expenditure which currently has a list price of one and a half million dollars ($1,500,000)?
a. The prevailing annual interest rate is four percent (4%).
b. The rate of inflation is assumed to be five percent (5.0%) per year for this type of equipment.
c. The anticipated expenditure will be paid all at once, that is, it will not be purchased on 'credit' in a manner of speaking.

Answer 1

Answer:

The monthly savings considering the inflation will be for 35,089.94 dollarsper month

Explanation:

the cost of the equipment will be

$Principal \: (1+ r)^{time} = Amount$

Principal 1,500,000.00

time 4 years

inflation 0.05000

$1500000 \: (1+ 0.05)^{4} = Amount$

Amount 1,823,259.38

This is the future value we need to reach in order to pay the medical equipment at once.

We will calculate the couta of a future value of 1,823,259.38 with 48 monthly payment at 4% annual interest rate:

$FV \div \frac{(1+r)^{time} -1}{rate} = C$

FV  $1,823,259.38

time 48

rate 0.003333333

$1,823,259.38 \div \frac{(1+0.003333)^{48} -1}{0.003333} = C$

C  $ 35,089.942