Bilbo Baggins wants to save money to meet three objectives. First, he would like
ID: 2623541 • Letter: B
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 $32,000 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 $420,000. Third, after he passes on at the end of the 25 years of withdrawals, he would like to leave an inheritance of $1,350,000 to his nephew Frodo. He can afford to save $4,100 per month for the next 10 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 11 through 30? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
Explanation / Answer
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 $24,000 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 $340,000. Third, after he passes on at the end of the 25 years of withdrawals, he would like to leave an inheritance of $1,500,000 to his nephew Frodo. He can afford to save $2,500 per month for the next 10 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 11 through 30?
answer
i = 10%/12
N = 10years*12 = 120 months
What are his savings equivalent by the end of year 10:
F10 = A*(F/A,10%/12,120) = 2,500*(204.8450) = 512,112.5
Net money he will have at the end of year 10:
P10 = 512,112.5 - 340,000 = 172,112.5
Moving that to the end of year 30 from year 10 (20 years = 240 months):
FV30 = P10*(F/P,i,N) = 172,112.5*(F/P,10%/12,240) = 172,112.5*(7.3281) = 1,261,257.61
*NOW WE NEED TO CALCULATE THE DEBT, TO SEE HOW MUCH IS NEEDED BY THAT PERIOD OF TIME:
Checking how much is needed for retirement (25 years = 300 months):
Pretirement = A*(P/A,i,N) = -24,000*(P/A,7%/12,300) = -24,000*(141.4869) = -3,395,685.6
PInheritance = F*(P/F,i,N) = -1,500,000*(P/F,7%/12,300) = -1,500,000*(0.1747) = -262,050
Equivalence of both by the end of year 30 from now = 3,395,685.6 + 262,050 = - 3,657,735.6
*So at year 30 we have: 1,261,257.61 - 3,657,735.6 = -2,396,477.99
Now we just need to calculate the equivalent A for the 15 years (180 months) of savings that are right before the end of year 30:
A = F*(A/F,i,N) = 2,396,477.99*(A/F,10%/12,180) = 2,396,477.99*(0.002413) = 5,782.7
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