What single investment made today, earning 12% annual interest, will be worth $6,000 at the end of 6 years? b. What is the present value of $6,000 to be received at the end of 6 years if the discount rate is 12%? c. What is the most you would pay today for a promise to repay you $6,000 at the end of 6 years if your opportunity cost is 12%? d. Compare, contrast and discuss your findings in parts a through c.

The results a-c  are the same $3,039.79  

However, the rate of return is given different names in each of the scenario.

In the first scenario, it was named annual interest which implies rate of return on an investment.

Annual interest is the same as discount rate because discounting an amount means stating in today's terms,which also applies to the amount to be invested when the future cash flow repayable is known, the amount to be invested can be brought back to equivalent amount today by discounting.

Finally, opportunity cost means the interest rate forgone by choosing to invest in one security,which is also the desirable rate of return convincing enough for the investment to be made.

A rate of return can be tagged annual interest, opportunity cost or discount rate,they are synonymous.

Explanation:

a.

The $6000 is the future value, the unknown is present value.

PV=FV*(1+r)^-N

r is the rate of return of 12% while N is 6 years

PV=$6000*(1+12%)^-6

PV=$3,039.79

b.the requirement also is PV with FV of $6,000 with discount rate of 12%,that rate of return,with N being 6 years

PV=$6000*(1+12%)^-6  

PV=$ 3,039.79  

c,The most to be paid for $6,000 with an opportunity cost of $12% is given below;

PV=$6000*(1+12%)^-6

    =$3,039.79  

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