Question

3) A leading broker has advertised money multiplier certificates that will triple your money in 9 years - that is, if you buy one for S333.33 today, it will pay you $1000 at the end of 9 years. What rate of return will you earn on these money multiplier certificates? You have an opportunity cost of 9% on your investments, and two alternatives to consider - $5,000 today OR S15,000 five years from today. a) If you were to receive the amounts, which alternative would you prefer? Why? b) If you had to pay the amounts, which alternative would you prefer? Why? 5) A firm purchases 100 acres of land for $200,000 and agrees to remit 20 equal annual end- of-year installments of $41,067 each. What is the implied interest rate on this loan?
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Answer 1

3. Rate of return earned on these money multiplier certificates = 12.98 %

Present value x ( 1 + r ) ⁿ = Future Value.

In the given situation , $ 1,000 / $ 333.33 = ( 1 + r ) ⁹

or ( 1 + r ) ⁹ = 3

r = 0.1298 or 12.98 %

4. Present value of $ 15,000 five years from today = $ 15,000 / ( 1.09) ⁵ = $ 15,000 x 0.64993 = $ 9,748.95

a. If you were to receive the amount, $ 15,000 five years from today is a better option, since the present value is greater than $ 5,000.

b. If you were to pay the amount, $ 5,000 today is a better option, as the present value of the payout of $ 5,000 is less than the present value of the payout of $ 15,000 five years from today.

5. Answer: 20 %

Present value interest factor of the annuity = $ 200,000 / $ 41,067 = 4.8701

Present value interest factor of an annuity is computed as [ { 1 - ( 1 / 1 + r ) ⁿ } / r ]

Therefore, [ { 1 - ( 1 / 1 + r ) ²⁰ } / r ] = 4.8701

r = 20 %