Kate Myers Solution
Case 7
Kate Myers
Purpose: The time value of money is a fundamental concept that must be understood by all business students. This case emphasizes the important variables to consider when saving for a down payment on a house and shows how these variables should dictate the actions of an individual.
1. Let,
PV = $98,000, n = 8 years, i = 4%.
Solving for future value via a calculator yields $134,119.77. 20% of this amount is Kate's required down payment.
($134,119.77)(.20) = $26,823.95.
2. Let,
FV = $26,823.95, the answer from question 1, i = .6666% (8%/12), the monthly return from the Merrill Lynch account, n = 96, (8*12), 8 years times 12 payments per year.
Solving for payment yields an answer of $200.38 per month.
3. This is the same procedure as question 2 with the exception that the compounding frequency has changed.
Let,
FV = $26,823.95, the answer from question 1, i = 8%, the annual return from the Merrill Lynch account, n = 8, 8 years of payments.
Solving for payment yields an answer of $2,521.85 per year. This amount is greater than 12 times the monthly payment because when Kate deposits funds at the end of each month, those funds are earning interest throughout the year, while funds deposited only at year's end are not accumulating interest.
For example, (12)($200.38) = $2,404.50.
$2,521.85 - $2,404.50 = $117.35. This additional amount represents the interest that the eleven $200.38 deposits would accrue throughout the year.
4-5. A table will better represent the sensitivity analysis performed in questions 4 and 5. The calculations are the same as those from question 2.
Home
Appreciation
Return on Merrill Lynch account
End-of-Month Required Deposit
2%
4%
$203.37
2%
8%
$171.55
2%
12%
$143.59
4%
4%
$237.55
4%
8%
$200.38
4%
12%
$167.73
6%
4%
$276.65
6%
8%
$233.36
6%
12%
$195.34
This sensitivity
Kate Myers
Purpose: The time value of money is a fundamental concept that must be understood by all business students. This case emphasizes the important variables to consider when saving for a down payment on a house and shows how these variables should dictate the actions of an individual.
1. Let,
PV = $98,000, n = 8 years, i = 4%.
Solving for future value via a calculator yields $134,119.77. 20% of this amount is Kate's required down payment.
($134,119.77)(.20) = $26,823.95.
2. Let,
FV = $26,823.95, the answer from question 1, i = .6666% (8%/12), the monthly return from the Merrill Lynch account, n = 96, (8*12), 8 years times 12 payments per year.
Solving for payment yields an answer of $200.38 per month.
3. This is the same procedure as question 2 with the exception that the compounding frequency has changed.
Let,
FV = $26,823.95, the answer from question 1, i = 8%, the annual return from the Merrill Lynch account, n = 8, 8 years of payments.
Solving for payment yields an answer of $2,521.85 per year. This amount is greater than 12 times the monthly payment because when Kate deposits funds at the end of each month, those funds are earning interest throughout the year, while funds deposited only at year's end are not accumulating interest.
For example, (12)($200.38) = $2,404.50.
$2,521.85 - $2,404.50 = $117.35. This additional amount represents the interest that the eleven $200.38 deposits would accrue throughout the year.
4-5. A table will better represent the sensitivity analysis performed in questions 4 and 5. The calculations are the same as those from question 2.
Home
Appreciation
Return on Merrill Lynch account
End-of-Month Required Deposit
2%
4%
$203.37
2%
8%
$171.55
2%
12%
$143.59
4%
4%
$237.55
4%
8%
$200.38
4%
12%
$167.73
6%
4%
$276.65
6%
8%
$233.36
6%
12%
$195.34
This sensitivity