Time Value of Money and Present Value
Date: 14/11/2012
52. Annuities:
You are saving for the college education of your two children. They are two years apart in age; one will begin college 15 years from today and the other will begin 17 years from today. You estimate your children’s college expenses to be $23,000 per year per child, payable at the beginning of each school year. The annual interest rate is 5.5 percent. How much money must you deposit in account each year to fund your children’s education? Your deposits begin one year from today. You will make your last deposit when your oldest child enters college. Assume four years of college
Solution:
Cost of 1 year at university = 23,000
N=4
I=5.5%
PMT=23,000
CPT PV = 80,618.45
For the first child the PV = 80,618.45/ (1.055) ^14 = $38,097.81
For the second child the PV = 80,618.45/ (1.055) ^16 = $34,229.07
Therefore the total cost today of your children’s college expense will be the addition of the 2
= $72,326.88
This is the present value of my annual savings, which are an annuity, so to get the amount I am supposed to save each year would be:
PV=72,326.88
N=15
I=5.5
CPT PMT = 7,205.6
57. Calculating Annuity Values:
Bilbo Baggins wants to save money to meet three objectives. First, he would like to be able to retire 30 years from now with retirement income of $25,000 per month for 20 years, with the first payment received 30 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 10 years at an estimated cost of $350,000. Third, after he passes on at the end of the 20 years of withdrawals, he would like to leave an inheritance of $750,000 to his nephew Frodo. He can afford to save $2,100 per month for the next 10 years. If he can earn an 11 percent EAR before he retires and an 8 percent EAR after he retires, how much will he have to save each month in years 11 through 30?
Solution:
First we get the FV of the 2,100
52. Annuities:
You are saving for the college education of your two children. They are two years apart in age; one will begin college 15 years from today and the other will begin 17 years from today. You estimate your children’s college expenses to be $23,000 per year per child, payable at the beginning of each school year. The annual interest rate is 5.5 percent. How much money must you deposit in account each year to fund your children’s education? Your deposits begin one year from today. You will make your last deposit when your oldest child enters college. Assume four years of college
Solution:
Cost of 1 year at university = 23,000
N=4
I=5.5%
PMT=23,000
CPT PV = 80,618.45
For the first child the PV = 80,618.45/ (1.055) ^14 = $38,097.81
For the second child the PV = 80,618.45/ (1.055) ^16 = $34,229.07
Therefore the total cost today of your children’s college expense will be the addition of the 2
= $72,326.88
This is the present value of my annual savings, which are an annuity, so to get the amount I am supposed to save each year would be:
PV=72,326.88
N=15
I=5.5
CPT PMT = 7,205.6
57. Calculating Annuity Values:
Bilbo Baggins wants to save money to meet three objectives. First, he would like to be able to retire 30 years from now with retirement income of $25,000 per month for 20 years, with the first payment received 30 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 10 years at an estimated cost of $350,000. Third, after he passes on at the end of the 20 years of withdrawals, he would like to leave an inheritance of $750,000 to his nephew Frodo. He can afford to save $2,100 per month for the next 10 years. If he can earn an 11 percent EAR before he retires and an 8 percent EAR after he retires, how much will he have to save each month in years 11 through 30?
Solution:
First we get the FV of the 2,100