PLEASE SHOW WORK USING THE FORMULAS BELOW: 1- You love travelling and have decid

Question

PLEASE SHOW WORK USING THE FORMULAS BELOW: 1- You love travelling and have decided to join the 7 continent travel club. Over the course of the next 7 years, you will go on a guided tour on each of the seven continents. The cost for the trip the first year is $12,000 and is payable today. After that, the trip costs will increase 3% per year for the 6 remaining years The club gives three options for payment. Assuming a 5% interest rate, which option would you choose? A) Seven (7) annual payments beginning with the $12,000 payment today. The payments will increase 3% per year B) One payment of $78,000 today and no additional payments for the remaining 7 years C) One payment of $108,500 7 years from today 2- You plan to take a year off to hike the Appalachian Trail. You believe that it will cost $4,500 to buy gear and food for the trip. You have $4,000 in your savings account and the bank pays an interest rate of 4% APR compounded quarterly. you have enough money for your trip? A) Less than one year B) Between 1 and 2 years C) Between 2 and 3 years D) Between 3 and 4 years 3- You receive $8,000 every six months beginning six months from today for 10 years and an additional $2,500 10 years from today. If the interest rate is 3.0% (EAR), which of the following is closest to the present value (PV) of this stream of cash flows? A) $137,499 B) $139,360 C) $144,148 D) $146,191 FORMULAS ry, = C(1 + r)n Future Value of a Cash Flow Present Value of Future Cash Flow Present Value of a Perpetuity Present Value of an Annuity Cash Flow in an Annuity PV r( 1-(1+r)n Present Value of a Growing Perpetuity 1+g 1+r Present Value of a Growing Annuity r-g APRYm Converting APR to EAR (APY) m = # compounding periods

Explanation / Answer

1)

option A) Statement showing Present value if amount is paid annually

option B) Payment of 78000$ today

Option C)

PV = FV(1+r)^n

=108500/(1.05)^7

=108500/1.4071

=77108.92$

Thus option C should be selected

2) here FV = 4500$, PV = 4000$, R= 4%/4 = 1%

FV = PV(1+1%)^n

4500 = 4000(1.01)^n

1.125 = (1.01)^n

assuming n = 11.88

(1.01)^11.88 = 1.125

Thus n = 11.88/4 = 2.97 years

Thus ans C) between 2 and 3 years

3)

Here n = 10*2 =20, A = 8000$ , r = 3%/2 =1.5%
PV(annuity) = A[1-(1/(1+r)^n) /r]
=8000[1-(1/1.015)^20 / 0.015]
=8000[1-0.74247/0.015]
=8000(17.16864)
=137349.1$
PV of amont to be received after 10 years
PV = 2500/(1.03)^10
=2500/1.343916
=1860.235$
PV of cash flow = 139209.3$

Year Payment PVIF @ 5% PV 0 12000 1 12000 1 12360 0.952 11771 2 12730.8 0.907 11547 3 13112.72 0.864 11327 4 13506.11 0.823 11112 5 13911.29 0.784 10900 6 14328.63 0.746 10692 Total payable 79350

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