1. Your friend finds a used Toyota Prius on CraigsList. He purchases it for $16,
ID: 2541955 • Letter: 1
Question
1. Your friend finds a used Toyota Prius on CraigsList. He purchases it for $16,000. He puts $1,000
down, finances the balance over 4 years for 5.95% interest, and will make monthly payments.
a. How much will his payments be each month?
b. How much principal and interest does he pay the first month?
c. What is the balance on his loan at the end of the first month?
2. A couple would like to take a cruise to Alaska, 15 months from now. They have $1500 in a savings
account. The savings account pays a nominal rate of 1%, compounded monthly.
a. If they start investing $110
today for 15 months
how much will they have 15 months
from today?
b.
If they start investing $110
a month from now for 15 months
how much will they
have 15 months from today?
c. If they need $3900 for the trip, how much would they need to invest each month, if
they make 15 monthly equal investments starting
a month from now
?
3. Bev’s Collectibles, a business that sells collectibles on eBay, has the following cash flows:
$-900
Initial investment in a PC, digital camera and photo
software (cash outflow, so enter as a negative into CF0)
$230
At the end of year 1
$630
At the end of year 2
$550
At the end of year 3
Assume that she could receive 6% annual interest, if she invested her money elsewhere.
a. What is the present value of the cash flows?
b. What is the future value of the cash flows?
Explanation / Answer
1.
(a)
Loan amount = $16,000 - $1,000 = $15,000
Monthly interest rate = 5.95%/12 = 0.496%
Number of payments to be made = 4 x 12 = 48
The amount of monthly payment can be determined by dividing the loan amount by the present value interest factor of an ordinary annuity of $1 per period at 0.496% for 48 periods.
Therefore,
Payment each month = Loan amount/PVIFA(0.496%,48) = $15,000/42.6202 = $351.95
(b)
Interest paid the first month = Loan amount x monthly interest rate = $15,000 x 0.496% = $74.40
Principal paid the first month = Monthly payment - interest = $351.95 - $74.40 = $277.55
(c)
Balance of loan at the end of first month = Loan amount - Principal paid the first month = $15,000 - $277.55 = $14,722.45
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