# Time Value of Money

It will cost \$20,000 a year for four years when an 8-year old child is ready for college. How much should be invested today if the child will make the first of four annual withdrawals 10-years from today? The expected rate of return is 8%. A) \$30,683. B) \$33,138. C) \$66,243. D) \$80,000 What is your answer? And why? Thanks!

B. 20K/(1.08^10) + 20K/(1.08^11) + 20K/(1.08^12) + 20K/(1.08^13) = 33137.75 And then I gave the guy a brochure for community college…

ok got it : the PV of the four 20K payments in 10years= -66 242 then u only need to find the PV of 66 242 now answer A hope it helps

humm … nahsuar’s view put trouble in me … anyone else please ? Edit: but i think he just found the PV of the fours payments now rather than 10 years from now. also he doesn’t take account of the growth in value of the investment made at t0

You first need to discount the \$20000 annuity for 4 year in order to obtain the PV=\$66243 After you calculate the present value of the lump sum (hence you solve for FV=\$66243) discounting the amount for 9 years (not 10 because it says “from today”). Hence you get B.

OOops !! 9 years NOT 10 years !! then PV= 33 138 well done strangedays

I calculate PV of 4 year withdrawal: PV = 20k/1.08^1 + 20/1.08^2+20/1.08^3+20/1.08^4 Then discount total withdrawal amount, discount rate 8% for 10 year. Choice: A

Thu…see my previous post B is correct.

Ok, i see. Time line helped me clear already Thanks strangedays

I don’t really get nahsuar’s method

nashuar calculated as an annuity due and than discounted for 10 periods, and that’s because end of year 9 is the same as beginning of year 10. Annuity due years 10, 11, 12 13, amount deposited immediatelly. Same thing.

thanks a lot guys! B is the right answer. i am having trouble getting the right time line. i discounted at 10 years instead of 9 years. strangedays pointed out “from today” hence it is 9. but i am encountering the same problem with the next question (QBank # 1580: Optimal Insurance is offering a deferred annuity that promises to pay 10 percent per annum with equal annual payments beginning at the end of 10 years and continuing for a total of 10 annual payments. For an initial investment of \$100,000, what will be the amount of the annual payments? A) \$25,937. B) \$42,212. C) \$38,375. D) 39,416. What is the number year you wuold discount once you have got the PV which is the FV of the initial 100,000?

Calculator in END mode PV=-10000, N=10, I/Y=10, PMT=0, CTP FV=259,374.25 Switch calculator in BGN mode PV=259,374.25, N=10, I/Y=10, FV=0, CPT PMT=38,374.51 Is it C?

map1 that is right. can you explain why switch to BGN mode, as nothing in the question text makes me to think it is an annuity due. it is so confusing!!

"equal annual payments beginning at the end of 10 years ", the end of the 10th year is the beginning of the 11th year, and the following 9 beginning of years (to total 10 years of payments).

Suny, It said “that promises to pay 10 percent per annum with equal annual payments beginning at the end of 10 years and continuing for a total of 10 annual payments” Annuity due begins at the end of 10 years means at end of year 10th it appears. I myself get this confusing too.