Time Value of Money and End-of-year Loan Payment

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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 $...
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