You are preparing yourself for the high costs of college tuition for your daught

Question

You are preparing yourself for the high costs of college tuition for your daughter. You expect him to start college in 18 years (t=18) and expect her to be in college for 4 years. Today’s tuition is $28,000 per year and tuition has increased historically at 6% per year and is expected to continue to grow at the same rate in the future. You want to make an initial deposit of $15,000 in a savings account, which is guaranteed to return 1.982% per year (APR) in interest, compounded monthly. Each year, until your daughter starts college you plan on depositing an equal amount that is precisely enough to make the tuition payments during the time your daughter attends college. Hence, your first deposit (not including the initial $15,000) takes place at t=1 and your final deposit takes place at t=17.

a. Calculate what annual deposit is required to achieve your goal.

b. Calculate how much money (at t=0) can be saved (or is lost?) when your son could skip a grade in high school and start college one year sooner?

Explanation / Answer

So, first we need to estimate the amount required at T-18 to finance the education.

We know that $28,000 per year is the current tution fees which will increase at the rate of 6% per year.

So, using finance calculatar, PV=28,000 , N=18 , I/Y 6% , PMT 0, Calculate FV we get $79,921.50.

So, this is the cost for T=18, we will be incurring this cost plus 6% in T=19 and so on which we also need to discount to get the amount of investment required at T=18.

So, our calculation will be like :-

So, we require $339,080 at T=18

Now again using finance calculator we will calculate PMT i.e the payment required per year to meet the expenditure.

FV = 339,080.09

I/Y = 1.982%

PV (Initial Payment) = (15,000)

N = 17

Calculate PMT = $18,017 (This will be close approximated deposit we need to make per year to meet the required expenditure)

b. So, for this we again need to go through the whole process again, we will first calculatethe expenditure required at T=17 by compounding $28,000 at 6% the same way we did for 18 years earlier. So, we are getting tution fees at T=17 as $75,397.64

Now if we calculate the remaining payment at T=18 we get the following table :-

So, we can see now we require $319,886.86

Now we need to calculate how much money can be saved at T=0, where we were investing 15,000 earlier. So, we will be using the PMT amount same as we got in last question i.e. $18,017.

Now, we using finance calculator

PMT = -18,017

FV = 319,886.86

I/Y = 1.982%

N=16

Calculate PV = 11,888.94

So, we are saving (15,000-11,888.94) = $3,111 initially.

Time Period Rate of Increase in Tution Fees Tution Fees Discount Rate Present value at t=18 18    79,921.50                      79,921.50 19 6%    84,716.79 1.98%                      83,070.37 20 6%    89,799.80 1.98%                      86,343.19 21 6%    95,187.79 1.98%                      89,745.03 Total amount required at t=18                    339,080.09

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.