Download HW02

林君達
H34945018
工程經濟
6/24/2017
4.7 As a typical middle-class consumer, you are making monthly payments on your
home mortgage (9% annual interest rate), car loan (12%), home improvement loan
(14%), and past-due charge accounts (18%). Immediately after getting a $100
monthly raise, your friendly mutual fund broker tries to sell you some investment
fund with a guaranteed return of 10% per year. Assuming that your only other
investment alternative is a savings account, should you buy?
Yes.
4.27 Suppose a young newlywed couple is planning to buy a home two years from
now. To save the down payment required at the time of purchasing a home worth
$220,000 (let's assume that the down payment is 10% of the sales price, or 22,000),
the couple decides to set aside some money from each of their salaries at the end of
every month. If each of them can earn 6% interest (compounded monthly) on his or
her savings, determine the equal amount this couple must deposit each month until the
point is reached where the couple can buy the home.
6% Compounded Monthly = 0.5% Monthly
N = 24 months
Target = $22,000
A = $22,000 (A/F, 0.5%, 24) = $828.34
4.37 Sam Salvetti is planning to retire in 15 years. Money can be deposited at 8%
compounded quarterly. What quarterly deposit must be made at the end of each
quarter until Sam retires so that he can make a withdrawal of $25,000 semiannually
over the first five years of his retirement? Assume that his first withdrawal occurs at
the end of six months after his retirement.
8% Compounded Quarterly = 2% Interest per quarter
$25,000 semiannually over five years = $25,000 x 10 = $250,000 = F
Amount needed at the end of 15 years = $149,829.81
N = 15 years x 4 = 60
A = $149,829.81 (A/F, 2%, 60) = $1,276.97
-1-
林君達
H34945018
工程經濟
6/24/2017
4.47 An automobile loan of $20,000 at a nominal rate of 9% compounded monthly for
48 months requires equal end-of-month payments of $497.70. Complete the following
table for the first six payments, as you would expect a bank to calculate the values:
9% Compounded monthly = 0.75% month
End Of Interest
Month Payment
Repayment Remaining Loan
of Principle Balance
1
$150.00
$347.70
$19,652.30
2
$147.39
$350.31
$19,301.99
3
$144.76
$352.94
$18,949.06
4
$142.12
$355.58
$18,593.48
5
$139.45
$358.25
$18,235.23
6
$136.76
$360.94
$17,874.29
4.57 To buy a $150,000 house, you take out a 9% (APR) mortgage for $120,000. Five
years later, you sell the house for $185,000 (after all other selling expenses). What
equity (the amount that you can keep before tax) would you realize with a 30-year
repayment term?
Total Amount = $150,000
Initial Loan = $120,000
APR = 9%
N = 360
Yearly Payment = PMT(9%,30,-120000) = $11,680.36
Remaining Loan on 5th year = $114,731.29
$185,000-$115,056.16-$30,000 = $5,268.71
-2-