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 a retirement income of $28,500 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 10 years at an estimated cost of $365,000. Third, after he passes on at the end of the 20 years of withdrawals, he would like to leave an inheritance of $1,225,000 to his nephew Frodo. He can afford to save $3,000 per month for the next 10 years. If he can earn an EAR of 11 percent before he retires and an EAR of 8 percent after he retires, how much will he have to save each month in Years 11 through 30? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

No. of years before retirement = 30 years

Retirement income = 28500/ month

No. of years after retirement = 20 years

EAR after retires = 8%

The total corpus required at the time of retirement can be calculated by using excel formula, PV(rate,nper,pmt,fv)

Rate	8% /12
nper	20 * 12
pmt	28500
Future value	0
Present value	3407297.31

After retirement, he would like leave an inheritance 0f 1225000

The present value after 30 years of that corpus will be:

Rate	8% /12
nper	20*12
pmt	0
future value	1225000
Present value	248639.95

10 years after retirement he would like to purchase a cabin, estimated cost 365000

The present value of that amount will be:

rate	8% /12
nper	10 *12
pmt	0
future value	365000
present value	164441.06

The total corpus required after 30 years = 3407297.31 + 248639.95 + 1644411.06 = 3820378.33

Savings:

after 10 years, the savings can be calculated by using excel formula: FV(rate,nper,pmt,pv)

rate	11% /12
nper	10*12
pmt	3000
present value	0
Future value	650994.42

To accumulate the total corpus, the monthly payment for the next 20 years can be calculated by using excel formula, PMT(rate,nper,pv,fv)

Rate	11% /12
nper	20*12
present value	650994.42
Future value	3820378.33
PMT	2306.12