Question

zoom in and it's clear. Thanks !

L LLLLLLL Decision #1: Which set of Cash Flows is worth more now? Assume that your grandmother wants to give you generous gift. She wants you to choose which one of the following sets of cash flows you would like to receive: Option A: Receive a one-time gift of $ 10,000 today. Option B: Receive a $1500 gift each year for the next 10 years. The first $1400 would be received 1 year from today. Option C: Receive a one-time gift of $18,000 10 years from today. Compute the Present Value of each of these options if you expect the interest rate to be 3% annually for the next 10 years. Which of these options does financial theory suggest you should choose? Option A would be worth $_ today. Option B would be worth $ today. Option C would be worth $_ today. Financial theory supports choosing Option Compute the Present Value of each of these options if you expect the interest rate to be 6% annually for the next 10 years. Which of these options does financial theory suggest you should choose? Option A would be worth $_ today. Option B would be worth $ today. Option C would be worth $ _today. Financial theory supports choosing Option

yes i believe $1400 first payment and than $1500 there after. It'd be much appreciated if you could also do $1500 for all payments. thank you!

Answer 1

Decision 1:

Interest rate 3% annually

i) Option A would be worth $ 10000 today

ii) Option B would be worth = 1400/(1.03) + 1500*(1-(1/(1.03)^9))/0.03)*(1/1.03)

= $ 12698.22 today

If $1500 were paid for 10 years, then it would be worth = 1500*(1-(1/(1.03)^10))/0.03)

= $ 12795.3 today

iii) Option C would be worth = 18000/(1/1.03^10)

= $ 13393.69 today

Financial theory supports choosing Option C

Interest rate 6% annually

i) Option A would be worth $ 10000 today

ii) Option B would be worth = 1400/(1.06) + 1500*(1-(1/(1.06)^9))/0.06)*(1/1.06)

= $ 10945.80 today

If $1500 were paid for 10 years, then it would be worth = 1500*(1-(1/(1.06)^10))/0.06)

= $ 11040.15 today

iii) Option C would be worth = 18000/(1/1.06^10)

= $ 10051.02 today

Financial theory supports choosing Option B

Interest rate 9% annually

i) Option A would be worth $ 10000 today

ii) Option B would be worth = 1400/(1.09) + 1500*(1-(1/(1.09)^9))/0.09)*(1/1.09)

= $ 9534.68 today

If $1500 were paid for 10 years, then it would be worth = 1500*(1-(1/(1.09)^10))/0.09)

= $ 9626.55 today

iii) Option C would be worth = 18000/(1/1.09^10)

= $ 7603.38 today

Financial theory supports choosing Option B

Decision 2

Interest rate is 7.2 % annually

a) The total worth after 35 years = 3000 * ((1.072)^35 - 1)/0.072

= $ 433237.79

b) If they put $ 3000 for the next 10 years, they would have = 3000* ((1.072)^10 - 1)/0.072

= $ 41842.97

b2) With no additional investments, $ 41842.97 would grow to = 41842.97*(1.072^35)

= $ 476913.95 after 35 years

c)If they put $3000 for the next 45 years, it would accumulate to = 3000 * ((1.072)^45 - 1)/0.072

= $ 910151.74

d) Coverting 7.2 % annually to per month rate

1.072 = (1+(i/12))^12

i = 0.00581 % per month

If they put $250 per month, after 45 years it will accumulate to = 250 * ((1.00581)^(45*12) - 1)/0.00581

= $ 939569.98

e) If they have save $ 1000000 for the first day of reitrement, the amount to be saved per year for 20 years is $ 23865.21.

1000000 = X * ((1.072^20)-1)/0.072

X = $ 23865.21