Unformatted text preview: Homework 21 Solution
1. A recent advertisement for a Dell computer is shown below. If you purchase the computer outright,
you’ll pay $1443. If you purchase the computer using their purchase plan (and, thanks to good credit,
get their lowest rate of $43/month) what will be the true cost of your loan? Express your answer as an
APY. The $1443 is the loan amount. The repayment plan consists of 45 equal monthly payments. So $1443 $43 P  A,i%, 45 P  A,i%, 45 $1443 $43 33.5581 Looking through the tables at the back of the textbook: P  A,1.25%, 45 34.2582
33.5581 32.5523 P  A, i %, 45 33.5581 i 1.50% 1.25% 1.50% 1.35% month 34.2582 32.5523 P  A,1.50%, 45 32.5523
APY 1 i 1 1.0135 1 17.5% year
M 12 2. The actual Dell advertisement (below) included the phrase “No payments for 90 days” which means
your 45 monthly loan payments don’t start until the end of Month 3. Under this new repayment plan,
what will be the true cost of your loan? Express your answer as an APY. Be sure to draw a cash flow
diagram! The first payment would normally be due at the end of Month 1, but now it’s not due until the end of
Month 3, so the cash flows are pushed two months into the future. To convert this new payment plan
to a present value at the end of Month 0, we have to discount it two years:
$1443 $43 P  A,i%, 45 P  F,i%, 2 Rearranging to get everything on the lefthand side: $43 P  A,i%, 45 P  F,i%, 2 $1443 0 P  A,i%, 45 P  F,i%, 2 33.5581 0
Let’s start at 1% per month and see where that leads us: P  A,1%, 45 P  F,1%, 2 33.5581 1.825
36.0945 0.9803 We’re a bit too high. Since PA and PF ↓ as the interest rate ↑, lets try the next higher interest rate: P  A,1.25%, 45 P  F,1.25%, 2 33.5581 0.139
34.2582 0.9755 0 1.825 i 1.00% 1.25% 1.00% 1.23% per month 0.139 1.825 APY 1 i 1 1.0123 1 15.8% year
M 12 3. Karen purchased 100 shares of Google, Inc. (GOOG) on March 1, 2006 for $337.50 per share. Four
years later, she sold those shares for $532.69 each. What was her annual return on investment? Give
your answer to the nearest 0.1% per year.
Setting the initial investment amount equal to the present value of the sale proceeds:
$337.50 100 $532.69 100 1 i 1 i 4 4 $337.50 0.6336
$532.69 1 i 0.6336 i 0.6336 1 4 1 4 1 0.1209 12.1% per year 4. Kelvin purchased 100 shares of IBM, Inc. (IBM) on Feb 8, 2005 at $93.30 per share. That was the
exdividend date for the first quarter of 2005, which means the day after the quarterly dividend was
paid. Kelvin saw the stock market crash coming and sold his IBM shares on Aug. 6, 2008 (just after
being paid his 14th quarterly dividend), at a price of $128.81 per share. If the quarterly dividend
during that time was $0.30 per share, what was Kelvin’s annual return on his IBM investment?
Equating the initial investment amount to the present value of the sales proceeds and the 14 quarterly
dividends:
P $93.30 100 $0.30 100 P  A,i%,14 $128.81100 P  F,i%,14 Therefore, the equation we are trying to solve for i% is $30 P  A,i%,14 $12,881 P  F,i%,14 $9330 0
If we ignore the dividend, the stock price appreciation alone would be:
$9330 1 i $12,881 i 2.33% per quarter
14 So let’s start at 2% and work our way up from there:
12.1062 0.7579 11.2961 0.6611 $30 P  A, 2%,14 $12,881 P  F, 2%,14 $9330 $796
$30 P  A,3%,14 $12,881 P  F,3%,14 $9330 $475 0 796 i 2% 1% 1% 0.626 2.626% per quarter 475 796 Converting this to an equivalent annual yield:
ROI = (1.02626)4 – 1 = 10.9% per year
5. What if Kelvin hadn’t seen the crash coming? Assume he had to sell his shares on Feb. 6, 2009 (just
two quarters later) at $91.47 per share. What would his annual return on investment have been?
HINT: Start with an interest rate of zero and note that (PF,0%,n) = 1 and (PA,0%,n) = n.
Equating the purchase price to the sale price and the 16 quarterly dividends:
$93.30 100 $0.30 100 P  A,i%,16 $91.47 100 P  F,i%,16 Therefore, the equation we are trying to solve for i% is
$30 P  A,i%,16 $9147 P  F,i%,16 $9330 0
Starting with an interest rate of zero and going up from there:
16 1 $30 P  A,0%,16 $9147 P  F,0%,16 $9330 $297
15.6650 0.9608 $30 P  A,0.25%,16 $9147 P  F,0.25%,16 $9330 $72 0 297 i 0% 0.25% 0.25% 0.805 0.201% per quarter 72 297 Converting this to an equivalent annual yield:
ROI = (1.00201)4 – 1 = 0.806% per year ...
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 Fall '08
 Moore,L
 Annual Percentage Rate, Kelvin, equivalent annual yield

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