Question

6.         Now, Let's assume that the couple would delay taking that vacation until summer 2022, where the cost would increase to $10,000, and let's also assume that their friend Kim has just made an offer to deliver $10,000 to the couple upon their arrival at Geneva Airport on the first of June, 2022. Kim's offer is a proposal of an alternative payment of a personal loan of $7,500 that she got from the couple in 2015. The agreement then was that the loan had to be paid back by Summer of 2022 with a compound interest rate of 5% annually.

A.        What would be the current value of the $10,000 assuming the compound interest rate stays at 5%?

B.        What would be the discount factor, and what does it mean to the couple financially and in terms of their personal utility (satisfaction)?

C.        Is it worth it for the couple to accept Kim's offer? Discuss the financial and nonfinancial (convenience, for instance) aspects of the argument taking into          consideration the calculations of the pay-off amount in the original deal 0f 2015.

7.         If the couple draws a new plan of saving for that vacation by putting aside $200 at the end of each month for the next three years, and if the cost of vacation stays the same as ($9,384.44), and the interest rate is 11% compounded annually, would the couple be able to take that vacation in 2019?

8.         What must their annuity be in order to make it to their vacation in 2021 if the interest rate is 15% compounded semiannually.

Answer 1

Answer 6 A) PV = Cash flow/ (1+r)^n , n= time = 2022-2015 = 7 years

= > PV = $10000 / ( 1+0.05)^7 = 7106.813 = $ 7107

Answer 6 B) DIscount factor is rate of return to make the PV and FV equal .

FV = PV (1+r) ^ 7

=> (10,000/ 7500 )^ (1/7) =1+r

=> r= 4.195% = 4.2%.

The couple is getting only 4.2% annual return instead of expected return of 5%.

Answer 6 C)  It is not worth for the couple to accept Kim's offer for couple , financially the return is lesser than the expected return.

Non financially : KIM don't have any track record of repayment. It is better to invest withorganized sector and institutions.

Answer 7) The concept is based on future value annuity, monthly payment of $200 for 36 months , with interest rate of 11%= 11/12= 0.92% monthly .

matirity amount calculated by use of = FV(rate,Nper,pmt) function ,

FV( 0.92%,36,200) =$8489.81 = $8,490.

Answer 8)

Here, the cost of vacation = $9,384.44 required in 2021 from now (2015) .

The monthly annuity required for (2021-2015=6 years = 72 months)

The same will calculated by use of PMT( rate, Nper, amount)

Rate = 15% compounded semiannually => effect Interest rate = 15.56 annual

=> 0.0129 monthly rate .

required amount = PMT( 0.0129%, 72 , 9384.44) = $ 130.95