Question

I've answered questions 1-4 (answers are bolded) but I am stuck on 5 and 6. Any help is appreciated. Thank you

Assume i=10%

1. Today (t=0) your daughter is born (congratulations and good luck with that!) and you decide to start saving for her education. You figure that you will need to pay for 5 years of undergraduate engineering at $20,000 per year (from t=18 through t=22), and two years for graduate school at $30,000 per year (t=23 and t=24). How much needs to be in her education account at t=18 to fund her education in full? (Answer: B)

a) 117,960 b) 118,960 c) 119,960 d) 120,960

2. Using your answer from Q.1, continue: Your parent offers to share the education costs equally with you. Your parent deposits the necessary sum (for their portion of the total amount) in an account on her birth date (t=0). How much did they deposit? (Answer: A)

a) 10,698 b) 10,787 c) 10,878 d) 11,021

3. Using your answer from Q.1, continue: You decide to fund your half by depositing equal amounts every year from her birth date to her 18th birthday (from t=0 up to and including t=18 deposits). You expect to have to skip the deposit on her 10th birthday due to extra expenses that year. How much do the annual deposits need to be? (Answer: B)

a) 1160 b) 1214 c) 1303 d) 1469

4. Suppose instead of the plan in Q#3, that you decide to start your equal-sum deposits on her 5th birthday. You will also plan to continue the equal-sum deposits all the way through to her 24th birthday (so including t=5, including t=10, and including t=24). How much do the annual deposits need to be in this case? (Answer: D)

a) 1750 b) 1780 c) 1810 d) 1840

5. Suppose instead of the plan in Q#4 that you decide to start your deposits on her date of birth but you increase them by $100 every year until the final deposit on her 18th birthday. What is the value of her first deposit?

a) 494 b) 514 c) 534 d) 554

6. Suppose instead of the plan in Q#5 that you decide to start your deposits on her 6th birthday. On her 6th birthday, you deposit X and you increase X by 6% each year until your final deposit on her 18th birthday. Find X.

a) 1803 b) 1823 c) 1843 d) 1863

Answer 1

5. The amount is X

P = X + (X+100)/1.1 + (X+200)/1.1^2 + .... + (X + 1800)/1.1^18

10,698 = X + X(P/A,10%,18) + 100(P/A,10%,18) + 100(P/G,10%,18)

First deposit = $ 534

Option C.

6. You start depositing the amount from the start of 6th year till 18th year.

Here P = $ 10,698

Option A.

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