Question

Assume that you are graduating, that you plan to work for 4 years, and then to go to law school for 3 years. Right now, going to law school would require $17,000 per year (for tuition, books, livingexpenses, etc.), but you expect this cost to rise by 8 percent per year in all future years. You now have $25,000 invested in an investment account which pays a simple annual rate of 9 percent, quarterlycompounding, and you expect that rate of return to continue into the future. You want to maintain thesame standard of living while in law school that $17,000 per year would currently provide. You plan tosave and to make 4 equal payments (deposits) which will be added to your account at the end of eachof the next 4 years; these new deposits will earn the same rate as your investment account currentlyearns. How large must each of the 4 payments be in order to permit you to make 3 withdrawals, at thebeginning of each of your 3 years in law school?

(Note: (1) The first payment is made a year fromtoday and the last payment 4 years from today, (2) the first withdrawal is made 4 years from today, and(3) the withdrawals will notbe of a constant amount.)

a.$13,242.67

b.$6,562.13

c.$10,440.00

d.$7,153.56

Would like to learn to solve by financial calculator.

Answer 1

first we need to calculate the future value at each time periods (T=4,5,6, as this is the time of study) to calculate the withdrawals for law school costs.

First year of college is at T=4(after 4 years of work)

Using the financial calculator

At T=4

N = 4, PV = -17000, I/Y = 8%, FV = ?

To calculate FV, give the above mentioned inputs and then,

press [CPT] and then press FV

we get FV at 4 = 23,128.31

Similarily

At T= 5

N = 5, PV = -17000, I/Y = 8%, FV = ?

FV at year 5 = 24,978.58

At T= 6

N = 6, PV = -17000, I/Y = 8%,PMT = 0, FV = ?

FV at year 6 = 26,976.86

Now the annual interest rate = 9%

Effective annual rate = (1+r/n)^n - 1

r = 9%

n = 4 (as it is quarterly compounding)

Effective annual = 9.3083 (roughly 9.31 %)

Now use the calculator again to find the NPV of the cash flows (FV at 4,5,6)

Press CF

CF0 = 23,128.31 press [ENTER] and then press down arrow([INS] button)

CF1 = 24,978.58 press [ENTER] and then press down arrow([INS] button)

F01 = 1 press [ENTER] and then press down arrow([INS] button)

CF2= 26,976.86 press [ENTER] and then press down arrow([INS] button)

F02 = 1 press [ENTER] and then press down arrow([INS] button)

Now press NPV

I = 9.31

press [ENTER] and then press down arrow([INS] button)

It reflects NPV

Press [CPT]

we get NPV as 68,556.73 (which is the present value at year 4 from T = 0)

Now determine the future value of the income from the job

N = 4, I/Y = 9.31, PV = -25000, PMT = 0

Press [CPT] and then press FV

we get FV as 35,692.72(lets denote it as FVj

So the difference between the NPV and FVj is the difference between amount required and the amount actually have in hand

= 68,556.73 - 35,692.72

= 32,864

Now we need to calculate the annuity payment for 32,864 ( as we need to accumulate this amount at year 4)

N = 4 , I/Y = 9.31, FV = 32,864, PV = 0

press [CPT] and then press PMT

we get the annuity amount as 7,153.55

Hence the answer to this is option D