Question 4 Would a dollar tomorrow be worth more to you today when the interest

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Question 4 Would a dollar tomorrow be worth more to you today when the interest rate is 22%, or when it is 14%? Show your work. a) If the interest rate is 10% what is the present value of a security that pays you $1,100 next year, $1,220 the year after, and $1,347 the year after that? b) c) A lottery claims its grand prize is S15 million, payable over 5 years at $3,000,000 per year. If the first payment is made immediately, what is the grand prize really worth? Use an interest rate of 4%. d) What is the yield to maturity (YTM) on a simple loan for $1,500 that requires a repayment of $3,000 in five years' time?

Explanation / Answer

1) Would a dollar tomorrow be worth more to you today when the interest rate is 22% or when it is 14%? Show your work.

Solution: It would be worth 1/(1 + 0.22) = $0.82 when the interest rate is 22%, rather than 1/(1 + 0.14) = $0.88 when the interest rate is 14%

Therefore, a dollar tomorrow is worth less with a higher interest rate today

2) If the interest rate is 10%, what is the present value of a security that pays you $1,100 next year, $1,220 the year after and $1347 the year after that?

Solution:

pv = 1,100 / 1.1 + 1220 / 1.1^2 + 1347/ 1.1^3 = 3020.29

3) A lottery claims its grand prize is $15 million, payable over 5 years at $3,000,000 per year. If the first payment is made immediately, what is this grand prize really worth? Use an interest rate of 4%

Solution: $3,000,000 + $3,000,000 / (1.04) + $3,000,000 / (1.04)^2 + $3,000,000 / (1.04)^3 + $3,000,000 / (1.04)^4 = $13,889,686

4) What is the yield to maturity on a simple loan for $1,500 that requires a repayment of $3,000 in five year's time

Solution:

1500 = 3000 / (1+i)^10

(1+i)^5 = 2

i = 14.9%

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