Paul Atreides wants to save money to meet three objectives. First, he would like to be able to retire 20 years from now with retirement income of $15,000 per month for 20 years, with the first payment received 20 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 10 years at an estimated cost of $100,000. Third, after he passes on at the end of the 20 years of withdrawals, he would like to leave an inheritance of $100,000 to Chani, his girlfriend. He can afford to save $3,000 per month for the next 10 years. If he can earn an 10 percent EAR before he retires and an 9 percent EAR after he retires, how much will he have to save each month in years 11 through 20? Note: To provide coherence and organization to your work, arrange your work for this question as follows: Step 1: Convert both EARS to annual nominal rates Step 2: Compute the amount needed at the 20-year mark from now Step 3: Compute the amount in hand at the 10-year mark from now Step 4: Compute the amount still required at the 10-year mark Step 5: Compute the shortage/surplus, if any, and compute the required monthly savings between years 11 through 20.
Paul Atreides wants to save money to meet three objectives. First, he would like to be able to retire 20 years from now with retirement income of $15,000 per month for 20 years, with the first payment received 20 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 10 years at an estimated cost of $100,000. Third, after he passes on at the end of the 20 years of withdrawals, he would like to leave an inheritance of $100,000 to Chani, his girlfriend. He can afford to save $3,000 per month for the next 10 years. If he can earn an 10 percent EAR before he retires and an 9 percent EAR after he retires, how much will he have to save each month in years 11 through 20? Note: To provide coherence and organization to your work, arrange your work for this question as follows: Step 1: Convert both EARS to annual nominal rates Step 2: Compute the amount needed at the 20-year mark from now Step 3: Compute the amount in hand at the 10-year mark from now Step 4: Compute the amount still required at the 10-year mark Step 5: Compute the shortage/surplus, if any, and compute the required monthly savings between years 11 through 20.
Chapter5: The Time Value Of Money
Section: Chapter Questions
Problem 19P
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Question
Transcribed Image Text:Paul Atreides wants to save money to meet three objectives. First, he
would like to be able to retire 20 years from now with retirement
income of $15,000 per month for 20 years, with the first payment
received 20 years and 1 month from now. Second, he would like to
purchase a cabin in Rivendell in 10 years at an estimated cost of
$100,000. Third, after he passes on at the end of the 20 years of
withdrawals, he would like to leave an inheritance of $100,000 to
Chani, his girlfriend. He can afford to save $3,000 per month for the
next 10 years. If he can earn an 10 percent EAR before he retires and
an 9 percent EAR after he retires, how much will he have to save each
month in years 11 through 20?
Note:
To provide coherence and organization to your work, arrange your work
for this question as follows:
Step 1: Convert both EARS to annual nominal rates
Step 2: Compute the amount needed at the 20-year mark from now
Step 3: Compute the amount in hand at the 10-year mark from now
Step 4: Compute the amount still required at the 10-year mark
Step 5: Compute the shortage/surplus, if any, and compute the required
monthly savings between years 11 through 20.
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