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 $21,000 per month for 20 years, with the first payment received 30 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 15 years at an estimated cost of $675,000. Third, after he passes on at the end of the 20 years of withdrawals, he would like to leave an inheritance of $500,000 to his nephew Frodo. He can afford to save $2,300 per month for the next 15 years.

   

Required:

If he can earn a 9 percent EAR before he retires and a 5 percent EAR after he retires, how much will he have to save each month in years 16 through 30? $8,815.19 $7,754.47 $7,602.42 $7,450.38 $8,291.47

Answer 1

Answer:

Correct answer is:

$7,602.42

Explanation:

First let us calculate retirement corpus required after 30 years from now:

Monthly payment at the end month = $21000

Retirement duration = 20 years = 20 * 12 months = 240 months

EAR = 5%

Monthly interest = (1 + 5%) ^1/12 - 1 = 0.4074123784%

At the end retirement period he would like to leave an inheritance of $500,000 to his nephew Frodo

Amount required at start of retirement = PV (rate, nper, pmt, fv, type)

= PV (0.4074123784%, 240, -21000, 500000, 0)

= $3,400,257.04

Amount required at start of retirement (30 years from now) = $3,400,257.04

Given that

He can save $2,300 per month for the next 15 years.

EAR = 9%

Monthly interest = (1 + 9%) ^1/12 - 1

= 0.72073233 %

Amount at the end 15 years = FV (rate, nper, pmt, pv, type)

= FV (0.72073233%, 180, -2300, 0, 0)

=$843,268.62

Given that he wants to purchase a cabin in 15 years at an estimated cost of $675,000

Hence balance left after 15 years = $843,268.62 - $675,000 = $168,268.63

Now we need to calculate monthly saving required each month in years 16 through 30 with initial balance of $168,268.63 to get a corpus of $3,400,257.04 at the end of 30 years

=PMT (rate, nper, pv, fv,type)

= PMT (0.72073233%, 180, 168268.63, -3400257.04, 0)

= $7,602.42

As such amount he will have to save each month in years 16 through 30 = $7,602.42

As such option C is correct and other options A, B, D and E are incorrect.