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hotpotato |
07/06/05 |
Hi expert, I have a question to ask you and I want to show you what
have done so I am on the right track. Can you please let me know if
i'm doing the right thing?
Tom and Kate are in the final stages of purchasing an all inclusive
honeymoon package to Mauritius. Hollywood Travel, the couple’s
travel broker, has quoted them a final price of $5,000. Due to
their current financial situation, Tom is planning on financing
their trip. Hollywood Travel has laid out two options for the couple
to choose from. The first option has the couple paying 25% interest
per year compounded quarterly, with equal payments every 3 months
for 2 years. The second option has Tom and Kate paying 26% interest
per year compounded monthly, with equal semi-annual payments for 4
years.
a) If Tom and Kate choose the first option by putting a down
payment of $1000 on the purchase of the trip, what would be their
equal quarterly payments?
b) If the couple choose to finance the entire vacation value,
which option will be more beneficial for Tom and Kate?
c) Hollywood Travel is planning on having a one-day
extravaganza next month where all honeymoon travel packages will be
financed at 0% interest. If Tom and Kate decide to hold off on
their honeymoon plans and take advantage of the sale, how much would
Hollywood Travel need to charge for their Mauritius trip during the
zero-interest sale in order to earn the usual combined return on the
sale and the financing?
option 1:
a) EAR (effective annual rate] = [1 + quoted rate /m]^ m - 1 where m
is number of times compounded
EAR = [1 + 0.25/4]^4 - 1
= 0.27443
down payment of 1000 = 5000 - 1000 = 4000
Present value annuity is:
PV = C x [1 -1/(1 + r)^t ]/r
where c is payments
4000 = C x [1 - 1/(1.27443)^2]/0.27443
C = 2856.40835 (payment per year)
divide by 4 for quarterly payments = 714.10209
option 2:
EAR = [1 + quoted r/m]^m - 1
[1 + 0.26/12]^12 - 1
=0.293333
4000 = C x [1 - 1/(1.29333)^4]/0.29333
C = 1825.92540 (payment per year)
-------------------------------------------------
b)option 1:
5000 = C * [1 - 1/(1.27443)^2]/0.27443
= 3570.51044 payment per year
Option 2:
5000 = C x [1 - 1/(1.29333)^4]/0.29333
=2282.40675 payment per year
option 2 more beneficial because cheaper
-------------------------------------------------
c) i'm not sure hwo you do c. Can you show me how? can you check if
teh above answers are correct? thanks so much! |
Clarification/Follow-up by hotpotato on 07/07/05 5:22 pm:
part a) i would have to calcuilate the effective annual rate which turns out to be 0.27443 compounded quarterly
1)my down payment of 1000 is equal to 5000-1000 = 4000
2) present value of annuity is 2856.40835
but i am paying quarterly which is 714.10209
part b) i need to find out how much to pay for the trip using the final price of 5000 because the couple chooses to finance the entire vacation.
the payment with option one = 3570.51044 / year
the payment with option two = 2282.40675 / year
since option 2 is cheaper, the couple should choose that because they pay lesser
part c) company wants to recover its cost financing so i would need the Present value of the future interest payments it is foregoing.
cost of the trip + Present value of future interest payments
I am not too sure how the calculations should be done. Can you show me the calculations?? thank you so much!
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