Time Value of Money and End-of-year Loan Payment
Fall 2012
Finc 414 (01)
Assignment no. : One
Time value of money
Please solve the attached problems
Date of Submission: Monday 10/09/2012
Please: No Late Submission
Solved By
Sherin Ezant
1. Accumulating a growing future sum
A retirement home at Deer Trail Estates now costs $ 185,000. Inflation is expected to cause this price to increase at 6% per year over the 20 years before G.L. Donovan retires. How large an equal, annual, end-of-year deposit must be made each year into an account paying an annual interest rate of 10% for Donovan to have the cash needed to purchases a home at retirement?
Solution:
Initial Present value of Price = $185,000 Inflation annual rate o increase= 6% Duration= 20 years
Using Table A-1 FV of 185,000 after inflation =185000*(3.207)= $593,295
Duration= 20 years Annual rate of return= 10% Annuity Ordinary=??
Using Table A-3 Annuity ordinary= 593,295/57.274= 10,358.88 to be paid at every year end
2. Deposits to create a perpetuity
You have decided to endow your favorite university with a scholarship. It is expected to cost $ 6,000 per year to attend the university into perpetuity. You expect to give the university the endowment in 10 years and will accumulate it by making equal annual (end-of-year) deposits into an account. The rate of interest is expected to be 10% for all future time periods.
• How large must the endowment be?
• How much must you deposit at the end of each of the next 10 years to accumulate the required amount?
Solution:
1st method:
PV of cost= 6,000 $
Duration= 10 years
Annual rate of return= 10%
Using perpetuity rule
• The endowment: 6000/10%= 60,000
• End of year annuity: 60,000/15.937= 3,764 $
Finc 414 (01)
Assignment no. : One
Time value of money
Please solve the attached problems
Date of Submission: Monday 10/09/2012
Please: No Late Submission
Solved By
Sherin Ezant
1. Accumulating a growing future sum
A retirement home at Deer Trail Estates now costs $ 185,000. Inflation is expected to cause this price to increase at 6% per year over the 20 years before G.L. Donovan retires. How large an equal, annual, end-of-year deposit must be made each year into an account paying an annual interest rate of 10% for Donovan to have the cash needed to purchases a home at retirement?
Solution:
Initial Present value of Price = $185,000 Inflation annual rate o increase= 6% Duration= 20 years
Using Table A-1 FV of 185,000 after inflation =185000*(3.207)= $593,295
Duration= 20 years Annual rate of return= 10% Annuity Ordinary=??
Using Table A-3 Annuity ordinary= 593,295/57.274= 10,358.88 to be paid at every year end
2. Deposits to create a perpetuity
You have decided to endow your favorite university with a scholarship. It is expected to cost $ 6,000 per year to attend the university into perpetuity. You expect to give the university the endowment in 10 years and will accumulate it by making equal annual (end-of-year) deposits into an account. The rate of interest is expected to be 10% for all future time periods.
• How large must the endowment be?
• How much must you deposit at the end of each of the next 10 years to accumulate the required amount?
Solution:
1st method:
PV of cost= 6,000 $
Duration= 10 years
Annual rate of return= 10%
Using perpetuity rule
• The endowment: 6000/10%= 60,000
• End of year annuity: 60,000/15.937= 3,764 $