4 - ROFantasy
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
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 Month|Interest Payment |Repayment of |Remaining Loan Balance |
| | |Principle | |
|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
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