Financial Mathematics Applications in Healthcare: Investment Analysis and Present Value Calculations for Nursing and Hospital Finance
Overview
This document provides worked solutions to financial mathematics problems relevant to healthcare professionals and hospital administrators. It demonstrates the application of compound interest formulas, future value calculations, and present value analysis to realistic scenarios involving investment deposits, mutual funds, and patient payment collections.
What this coursework covers
- REIT investment compound interest calculations over 5, 10, 15, and 20-year periods
- Mutual fund growth analysis at 8 percent annual rate for 3, 6, 9, and 12-year timeframes
- Present value of annuity calculations for patient payment collections at varying discount rates
- Donor contribution present value analysis using present value factor tables
Preview
Student
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Answers
- If a nurse deposits $12,000 today in a real estate investment trust (REIT) and the interest is compounded annually at 7 percent, what will be the value of this investment:
- Five years from now?
We use the formula:
A=P(1+r/100)^n
Where A = future value, P = present value, r = rate of interest, n= time period
Hence
A=12000*(1.07)^5
= $16,830.62(approx).
- Ten years from now?
A=12000*(1.07)^10
= $23,605.82(approx).
- Fifteen years from now?
A=12000*(1.07)^15
= $33,108.38(approx).
- Twenty years from now?
A=12000*(1.07)^20
= $46,436.21(approx).
- If a nurse deposits $24,000 today in a mutual fund that is expected to grow at an annual rate of 8 percent, what will be the value of this investment:
- Three years from now?
We use the formula;
Future value = present value (1+rateof interest/100)^time period
Hence
Future value= $24,000* (1+0.08)^3
= $24,000 * 1.259712
= $ 30,233.088
= $ 30,233.09
- Six years from now?
Future value= $24,000* (1+0.08)^6
= $24,000 * 1.586874323
= $38,084.98
- Nine years from now?
Future value= $24,000* (1+0.08)^9
= $24,000 * 1.999004627
= $47,976.11
- Twelve years from now?
Future value= $24,000* (1+0.08)^12
= $24,000 * 2.518170117
= $60,436.08
- If a hospital received $7,500 in payments per year at the end of each year for the next twelve years from an uninsured patient who underwent an expensive operation, what would be the current value of these collection payments:
- At a 4 percent rate of return?
Answer
4% rate of return
=c*[1-(1+i)^-n]/i
=7500*[1-(1.04)^-12]/0.04
=$70,388.05
- At an 8 percent rate of return?
8% rate of return
=c*[1-(1+i)^-n]/i
=7500*[1-(1.08)^-12]/0.08
=$56,250.