8. Consider the following alternatives: i. $100 received in one year ii. $200 received in 5 years iii. $300 received in 10 years a. Rank the alternatives from most valuable to least valuable if the interest rate is 10% per year. b. What is your ranking if the interest rate is only 5% per year? c. What is your ranking if the interest rate is 20% per year?

200 option > 300 option > 100 option

300 option > 200 option. > 100 option

100 option > 200 option > 300 option

Explanation:

Given that:

At 10% interest rate:

Amount / (1 + rate)^n ; n = Period ;

Amount of $100 in 1 year

100/(1 + 0.1)^1 = 90.909

Amount $200 in 5 years :

200/(1+0.1)^5 = 124.184

Amount $300 in 10 years :

300/(1+0.1)^10 = 115.663

$200 option > 300 option > 100 option

When rate = 5% per year

Amount of $100 in 1 year

100/(1 + 0.05)^1 = 95.238

Amount $200 in 5 years :

200/(1+0.05)^5 = 156.705

Amount $300 in 10 years :

300/(1+0.05)^10 = 184.174

300 option > 200 option. > 100 option

When rate = 20% per year

Amount of $100 in 1 year

100/(1 + 0.2)^1 = 83.333

Amount $200 in 5 years :

200/(1+0.2)^5 = 80.376

Amount $300 in 10 years :

300/(1+0.2)^10 = 48.452

100 option > 200 option > 300 option