Question

Consider the following​ alternatives: i. $ 140 received in one year ii. $ 240 received in five years iii. $ 350 received in 10 years a. Rank the alternatives from most valuable to least valuable if the interest rate is 11 % per year. b. What is your ranking if the interest rate is 1 % per​ year? c. What is your ranking if the interest rate is 20 % per​ year?

Answer 1

Answer and Explanation:

The computation is shown below:

The formula is

= Amount ÷ (1 + interest rate)^number of years

a) Rate = 11%

Value of $140 in 1 year = $140 ÷ (1 + 11%) = $126.13

Value of $240 in 5 years = $240 ÷ (1 + 11%)^5 = $142.43

Value of $350 in 10 years = $350 ÷ (1 + 11%)^10 = $123.26

Now Ranking

Opotion 2 > Option 3 > Option 1

b) Rate = 1%

Value of $140 in 1 year = $140 ÷ (1 + 1%) = $138.61

Value of $240 in 5 years = $240 ÷ (1 + 1%)^5 = $228.35

Value of $350 in 10 years = $350 ÷ (1 + 1%)^10 = $316.85

Now Ranking

Option 3 > Option 2 > Option 1

c) Rate = 20%

Value of $140 in 1 year = $140 ÷ (1 + 20%) = $116.67

Value of $240 in 5 years = $240 ÷ (1 + 20%)^5 = $96.45

Value of $350 in 10 years = $350 ÷ (1 + 20%)^10 = $56.53

Now Ranking

Option 1 > Option 2 > Option 3