Which of the following investments would have the highest future value at the en

Question

Which of the following investments would have the highest future value at the end of 10 years? Assume that the effective annual rate for all investments is the same and is greater than zero.

e. Investment E pays $250 at the end of every year for the next 10 years (a total of 10 payments).

a. Investment A pays $250 at the beginning of every year for the next 10 years (a total of 10 payments). b. Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments). c. Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments). d. Investment D pays $2,500 at the end of 10 years (just one payment).

e. Investment E pays $250 at the end of every year for the next 10 years (a total of 10 payments).

Explanation / Answer

For understanding the above question, consider the time value of money. Money in hand today is more valuable than money in hand tomorrow.

So $100 with you today will be worth more than $100 that you will receive after 10 days.

The $100 that you will receive after 10 days will have more worth than $100 that you will receive after 1 month.

So, money received at the beginning of a period (say year or month is more valuable than the same money received at the end of the period). So money recived at the beginning will also have the highest future value as it will get the benefit of additional time period for which the annual rate is applied.

option a and option c have payments being made at the beginning of the periods in question.

Assume the annual rate to be 10%

Future value in case of option a for the 1st year = 250*(1.1^10). for the 2nd year = 250*(1.1^9) and for the 10th year = 250*(1.1^1). Adding all of them we get the future value as $4382.80

For option c: payment is made at begining of every 6 months. applicable rate will be 5%. Total future value (using the same formula as above). Adding them we get the future value as $3261.9

So the answer is option "a"

Option a Option c Year Cash flow FV Year Cash flow FV 1 250 648.4356 0.5 125 203.6118 2 250 589.4869 1 125 198.7048 3 250 535.8972 1.5 125 193.916 4 250 487.1793 2 125 189.2427 5 250 442.8903 2.5 125 184.6819 6 250 402.6275 3 125 180.2311 7 250 366.025 3.5 125 175.8876 8 250 332.75 4 125 171.6487 9 250 302.5 4.5 125 167.512 10 250 275 5 125 163.4749 5.5 125 159.5352 Total 4382.8 6 125 155.6904 6.5 125 151.9383 7 125 148.2766 7.5 125 144.7031 8 125 141.2158 8.5 125 137.8125 9 125 134.4912 9.5 125 131.25 10 125 128.0869 Total 3261.9

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