2) (45 points) A married couple is expecting their first child and they want to

Question

2) (45 points) A married couple is expecting their first child and they want to start saving money for their child?s education. They want to be able to withdraw $100.000 per year for 4 years, starting 18 years from now They have identified a fund that is guaranteeing a return of 6% per year compounded monthly They would like to save a fixed amount per month for 15 years. starting one month from now Calculate their monthly deposit assuming that the fund will be depleted when the last annual withdrawal is made.

Explanation / Answer

Year Withdrawl Present Value 1 0.94190534 100000 94190.53 2 0.887185669 100000 88718.57 3 0.835644919 100000 83564.49 4 0.787098411 100000 78709.84 Total 345183.43 So after 18 year they must have 345,183.43 in order to withdraw 100,000 each year for 4 year Formula for 18 years annuity is A = P x (a^(18*12)-1)/a-1 Here A=345183.43 a = 1+6/1200 = 1.005 Hence, 345183.43 = P x (1.005^216-1)/(1.005-1) Or, 345183.43 = P x (1.93676597/0.005) Or, 345183.43 = P x 387.353194 Therefore P = 345183.43/387.353194 = 891.13 Their Withdrawl amounts are stated in the below table: Beginning Ending Year Amount Interest Withdrawl Amount 18 345183.43 21290.1589 100000 266473.59 19 266473.5927 16435.5081 100000 182909.10 20 182909.1009 11281.4331 100000 94190.53 21 94190.53397 5809.46603 100000 0.00

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