Bilbo Baggins wants to save money for retirement, a cabin, and inheritance for his nephew Frodo. He can save $2,700 per month for 10 years. To meet his objectives, he will need to save $3,873.69 per month for years 11 through 30.

1. Bilbo Baggins wants to save money to meet three objectives. First, he would like to be able to
retire 30 years from now with retirement income of $25,000 per month for 25 years, with the
first payment received 30 years and 1 month from now. Second, he would like to purchase a
cabin in Rivendell in 10 years at an estimated cost of $350,000. Third, after he passes on at the
end of the 25 years of withdrawals, he would like to leave an inheritance of $1,550,000 to his
nephew Frodo. He can afford to save $2,700 per month for the next 10 years. If he can earn an
EAR of 10 percent before he retires and an EAR of 7 percent after he retires, how much will he
have to save each month in years 11 through 30?
Solution
present value of retirement at end of 30 years
= 25000* 12 * [1-(1+7%)ˆ-25]/7% = 3496074.95
present value of retirement income now = 200355
present value of cabin now = 350000/(1.1)ˆ10 = 134940.15
present value of inheritance money = 1550000/(1.07)ˆ25 * 1/(1.1)ˆ30
= 16366.53
present value of saving of 2700 = 2700 *12 * [1-(1.1)ˆ-10]/0.1 = 199083.97
present value of remaining amount to save = 200355 + 134940.15 + 16366.53 - 199083.97
= 152577.71
present value of remaining amount to save after 10 years
= 152577.71 * 1.1ˆ10
= 395747.28 = x *12* [1-(1+10%)ˆ-20]/10%
=>

2. amount to save per month
= 3873.69