Question

LyftUrCash offers a unique service of connecting lenders and borrowers with no banking middleman. Fred is currently considering 2 offers both of which he evaluates using an annual discount rate of 11%. The first offer will guarantee him $7,500 in 5 years and the second will provide $10,000 in 7 years. He will use Present Value analysis to determine what to bid for each contract. Alternatively, he could invest those funds in a mutual fund for 6 years that historically has had an annual return of 9%. With that investment, he is considering both reinvesting what he earns each year or using the annual earnings to cover his car payments. How much would Fred earn over the life of the mutual fund investment if he reinvests the earnings each year rather than withdrawing them and the mutual fund maintains its average rate of return each year?

CALCULATED VARIABLES: simple = $5,005 pvboth = $9,268 pv2 = $4,817 pv1 = $4,451

Answer 1

In this question, PV of 1st investment opportunity is Calculated and given as: $4,451

and the PV of second investment opportunity is given as: $4,817

upon seeing the Present Value of both the opportunity it is clear that the second opportunity has more attractive PV than the first, hence Second opportunity should be considered.

Now, Alternatively Fred can invest both the funds($7,500 and $10,000) in a Mutual Fund which is giving average annual returns of 9% and it is maintaining this percentage of returns for over 6 years.

We have to calculate the amount earned by Investing in Mutual Funds for a period of 6 years and if the yearly earned amounts are also invested in the Mutual Fund not withdrawn.

Therefore,

Amount to be invested = $7500 + $10,000 = $17,500

Rate of returns = 9% per annum.

Period = 6years.

Amount at the End of 1st year = $17,500 * (1 + 0.09) = $19,075

Now in second year amount to be invested will change and it will be the amount which we get at the end of the 1st year.

Amount at the End of 2nd year = $19,075 * ( 1+ 0.09) = $20,791.75

Amount at the End of 3rd year = $20,791.75 * (1 + 0.09) = $22,663.0075

Amount at the End of 4th year = $22,663.0075 * (1+ 0.09) = $24,702.68

Amount at the End of 5th year = $24,702.68 * (1+0.09) = $26,925.92

Amount at the End of 6th year = $26,925.92 * (1+0.09) = $29,349.25

Therefore, the amount at the End of the Investment Horizon has become $29,349.25

Now Amount earned by investing in the fund = $29,349.25 - $17,500 = $11,849.25

Hence, the amount earned by investing in the Mutual Fund is $11,849.25.