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 $31,500 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 $415,000. Third, after he passes on at the end of 30 years, he would like to leave an inheritance of $1,375,000 to his nephew Frodo. He can afford to save $4,000 per month for the next 10 years. If he can earn an EAR of 10% before he retires and an EAR of 7% after he retires, how much will he have to save each month in years 11 through 30?

Answer is not $2,331.10, $3,024, or $3,122.15

Answer 1

EMR before retirement (1+10%)^(1/12)-1 0.00797414

EMR after retirement (1+7%)^(1/12)-1 0.005654145

PV of retirement income $4,544,729.25 PV(0.005654,300,31500,,)

PV of inheritance $76,463.41 415000/1.07^25

Total PV after 30 years $4,621,192.66

Value of saving 4000 per month for 10 yrs $799,455.43 FV(.007974,120,-4000,,)

Less: cabin cost $415,000.00

Available surplus $384,455.43

Money to be saved per month for 20 yrs $2,833.10 PMT(0.007974,240,-384455.43,4621192.66,)