Bilbo Baggins wants to save money to meet three objectives. First, he would like

Question

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 $26,000 per month for 30 years, with the first payment received 30 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 20 years at an estimated cost of $977,000. Third, after he passes on at the end of the 30 years of withdrawals, he would like to leave an inheritance of $550,000 to his nephew Frodo. He can afford to save $1,700 per month for the next 20 years.

If he can earn a 10 percent EAR before he retires and a 7 percent EAR after he retires, how much will he have to save each month in years 21 through 30?

Explanation / Answer

EAR = [1 + (APR/m)]m - 1

APR for working period is 9.57%

APR for retirement period is 6.78%

First, we need to calculate the money Bilbo need when he retires

Present Value = Present Value of Annuity + Present Value of Inheritance

= $26,000 x PVIFA + $550,000 x PVIF

= $26,000 x [{1 - (1 + 0.0678/12)-360} / (0.0678/12)] + [$550,000 / (1 + 0.0678/12)360]

= $3,996,350.918 + $72,359.212 = $4,068,710.13

Second, we need to calculate the money that bilbo save

Future Value = Future Value of Annuity

= $1,700 x FVIFA

= $1,700 x [{(1+0.0957/12)240 - 1} / (0.0957/12)]

= $1,700 x 718.35

= $1,221,202.615

Bilbo has saved $1,221,202.615. He pays $977,000 for the house.

That means that he has $244,202.615 left in his bank account.

Now , we can calculate how much will he have to save each month in years 21 through 30

Future Value = $244,202.615 x FVIF

= $244,202.615 x [ 1 + 0.0957/12]120

= $244,202.615 x 2.59

= $633,463.512

•Bilbo will have $633,463.512

•Bilbo needs $4,068,710.13

•There Bilbo needs to save $4,068,710.13- $633,463.512

•Needed savings $3,435,246.62

Future Value Annuity = PMT x FVIFA

$3,435,246.62 = PMT x [{(1 + 0.0957/12)120 - 1} / (0.0957/12)]

PMT = $3,435,246.62 / 718.35

PMT = $4,782.105

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.