Scott and Linda have been saving to pay for their daughter Casie's college education. Casie just...

Scott and Linda have been saving to pay for their daughter Casie's college education. Casie just turned 10 at (t = 0), and she will be entering college 8 years from now (at t = 8). College tuition and expenses at State U. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. Ellen should graduate in 4 years¾if she takes longer or wants to go to graduate school, she will be on her own. Tuition and other costs will be due at the beginning of each school year (at t = 8, 9, 10, and 11). So far, Scott and Linda have accumulated $15,000 in their college savings account (at t = 0). Their long-run financial plan is to add an additional $5,000 in each of the next 4 years (at t = 1, 2, 3, and 4). Then they plan to make 3 equal annual contributions in each of the following years, t = 5, 6, and 7. They expect their investment account to earn 9%. How large must the annual payments at t = 5, 6, and 7 be to cover Casie's anticipated college costs?

a. $2,412.76

b. $2,177.51

c. $1,965.21

d. $2,292.12

e. $2,068.64

Solutions

Expert Solution

College Tuition Fees would be due at the end of Year 8, Year 9, Year 10 and Year 11. The amount due today would be $ 14500 and is expected to grow at 3.5 % per annum.

Therefore, Expense at end of Year 8 = 14500 x (1.035)^(8) = $ 19093.73

Expense at end of Year 9 = 14500 x (1.035)^(9) = $ 19762.01

Expense at end of Year 10 = 14500 x (1.035)^(10) = $ 20453.68

Expense at end of Year 11 = 14500 x (1.035)^(11) = $ 21169.56

Discounted Value of College Expenses at the end of Year 8 = 19093.73 + 19762.01 / (1.09) + 20453.68 / (1.09)^(2) + 21169.56 / (1.09)^(3) = $ 70786.25

Combined Future Value of Initial Accumulation and annual deposits upto Year 4 = 15000 x (1.09)^(8) + 5000 x (1.09)^(7) + 5000 x (1.09)^(6) + 5000 x (1.09)^(5) + 5000 x (1.09)^(4) = $ 62165.16

Let the equal annual contributions be $ K

Therefore, K x (1.09)^(3) + K x (1.09)^(2) + K x (1.09) = 70786.25 - 62165.16

K x 3.573129 = $ 8621.09

K = 8621.09 / 3.573129 = $ 2412.756 or $ 2412.76 approximately.

Hence, the correct option is (a).

jeff jeffy answered 1 year ago

Next > < Previous

Related Solutions

ohn and Daphne are saving for their daughter Ellen's college education. Ellen just turned 10 (at...

ohn and Daphne are saving for their daughter Ellen's college education. Ellen just turned 10 (at t = 0), and she will be entering college 8 years from now (at t = 8). College tuition and expenses at State U. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. Ellen should graduate in 4 years--if she takes longer or wants to go to graduate school, she will be on her own....

John and Daphne are saving for their daughter Ellen's college education. Ellen just turned 10 at...

John and Daphne are saving for their daughter Ellen's college education. Ellen just turned 10 at (t = 0), and she will be entering college 8 years from now (at t = 8). College tuition and expenses at State U. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. Ellen should graduate in 4 years--if she takes longer or wants to go to graduate school, she will be on her own....

Jim and Elsie are saving for their granddaughter Amy’s college education. Amy just turned 12 (at...

Jim and Elsie are saving for their granddaughter Amy’s college education. Amy just turned 12 (at t = 0), and she will be entering college 6 years from now (at t = 6). College tuition and expenses at Sam Houston State University are currently $15,000 a year, but they are expected to increase at a rate of 2% a year. Amy should graduate in 4 years--if she takes longer or wants to go to graduate school, she will be on...

2. You are currently saving for your child's college education. The current cost of college is...

2. You are currently saving for your child's college education. The current cost of college is $10,000 a year. You expect that college costs will continue to increase at a rate of 5 percent a year. Your child is scheduled to begin attending a four-year college 10 years from now (i.e., college payments will be made at t=10, t=11, t=12, and t=13). You currently have $25,000 in an account which earns 6 percent after taxes. You would like to have...

You are currently saving for your child's college education. The current cost of college is $10,000...

You are currently saving for your child's college education. The current cost of college is $10,000 a year. You expect that college costs will continue to increase at a rate of 5 percent a year. Your child is scheduled to begin attending a four-year college 10 years from now (i.e., college payments will be made at t=10, t=11, t=12, and t=13). You currently have $25,000 in an account which earns 6 percent after taxes. You would like to have all...

A father is saving to put his daughter through college. She is 5 years old, will...

A father is saving to put his daughter through college. She is 5 years old, will enroll in 13 years, and should graduate 4 years after that. Assume all college costs are paid upfront at the beginning of the year annually. Currently, college costs $18,000 per year, but is expected to increase 3% per year. He currently has $10,000 saved and his account earns 8% annually. He plans on making 13 equal deposits starting one year from today. How large...

You are saving for the college education of your two children. They are two years apart...

You are saving for the college education of your two children. They are two years apart in age; one will begin college in 7 years, and another in 10 years. You estimate your first child’s college expenses to be $30,000 per year, paid at the beginning of each college year (first payment is at year 7 and so on). You estimate your second child’s college expenses to be $50,000 per year, paid at the beginning of each college year (first...

You are saving for the college education of your two children. They are two years apart...

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 21,000$ per year per child, payable at the beginning of each school year. It takes four years to graduate. The annual interest is 15%. How much money must you deposit in an account each year to fund...

You are saving for the college education of your two children. They are two years apart...

You are saving for the college education of your two children. They are two years apart in age; one will begin college 14 years from today and the other will begin 16 years from today. You estimate your children’s college expenses to be $38,000 per year per child, payable at the beginning of each school year. The appropriate interest rate is 6.8 percent. Your deposits begin one year from today. You will make your last deposit when your oldest child...

To pay his university education, Mr. Ahmed is saving $ 1000, at the beginning of each...

To pay his university education, Mr. Ahmed is saving $ 1000, at the beginning of each year for the next 7 years in a Bank Muscat account paying 10% interest rate. How much will Mr. Ahmed have in that account at the end of 7th year? Mr. Ahmed need $ 17000 to pay his university fees in future, justify your suggestion to him regarding his investment in Bank Muscat?

Subjects