# Respond to each classmate 100 words a piece.

Practice Problems

Ch 4 P1

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What is the present value of 23-year annuity of \$5,000 per year with the first cash flow received 3 years from now? Use a discount rate of 8%.

Or

We can use the PVA annuity equation to answer this question. The annuity has 23 payments, not 22 payments. Since there is a payment made in Year 3, the annuity actually begins in Year 2. So, the value of the annuity in Year 2 is:

PVA = C({1 – [1/(1 + r)]t } / r )

PVA = \$5,000({1 – [1/(1 + .08)]23 } / .08)

PVA = \$51,855.29

This is the value of the annuity one period before the first payment, or Year 2. So, the value of the cash flows today is:

PV = FV/(1 + r)t

PV = \$51,855.29 / (1 + .08)2

PV = \$44,457.56

P2

You are saving for the college education of your 2 children. They are 2 years apart in age: one will begin college 15 years from now and the other will begin 17 years from today. You estimate their college expense to be \$35,000 per child per year, payable at the beginning of the school year. The annual interest rate is 8.5%. How much money must you deposit in an account each year to fund your children’s education? Your deposits begin 1 year from now. You will make your last deposit when your oldest child enters college. Assume 4 years of college.

First, we will calculate the present value of the college expenses for each child. The expenses are an annuity, so the present value of the college expenses is:

PVA = C({1 – [1/(1 + r)]t } / r )

PVA = \$35,000({1 – [1/(1 + .085)]4 } / .085)

PVA = \$114,645.88

This is the cost of each child’s college expenses one year before they enter college. So, the cost of the oldest child’s college expenses today will be:

PV = FV/(1 + r)t

PV = \$114,645.88/(1 + .085)14

PV = \$36,588.29

And the cost of the youngest child’s college expenses today will be:

PV = FV/(1 + r)t

PV = \$114,645.88/(1 + .085)16

PV = \$31,080.12

Therefore, the total cost today of your children’s college expenses is:

Cost today = \$36,588.29 + 31,080.12

Cost today = \$67,668.41

This is the present value of your annual savings, which are an annuity. So, the amount you must save each year will be:

PVA = C({1 – [1/(1 + r)]t } / r )

\$67,668.41 = C({1 – [1/(1 + .085)]15 } / .085)

C = \$8,148.66

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