# Sample Essay Paper on Time Value of Money

##### How does the present value of a lump sum compare to the present value of an annuity?

The present value of a lump sum would mean that it is the discounting a single value that would be received once at the end of the investment period. This means that the present value interest factor would be subjected to the lump sum amount in order to get its present value. On the other hand, the notion present value of annuity is the discounting of a series of equal periodic payments which are deemed to be received throughout the investment period. In this prospect, the present value annuity factor would be utilized in order to get the present value of all those series of periodic payments.

How does the future value of an ordinary annuity compare to the future value of an annuity due?

For the ordinary annuity, the amounts payments are made at the end of the year meaning that the compounding to get the future value starts at the end of the year. it means therefore that the future value of the first payment is got by compounding the amounts using the maturity period of the investment. On the other hand, the annuity due is paid at the beginning of the year. It therefore means that for compounding purposes, the period that would be used would be the maturity period + 1 to inculcate the fact that the payments are made at the start of the year.

##### How does the present value of an annuity compare to the present value of an annuity due?

For the present value of ordinary annuity, the number of period that would be used for the discounting of periodic payment would be the maturity period of the investment. For the present value of the annuity due, we would subtract one period from the maturity period and only add on value of the periodic payment to the present value of other annuities since it is being paid at year zero (0). In so doing I would be treating the first payment as not being discounted for the period id at zero.

##### What’s the value today of \$500 received in 3 years if the going rate of interest is 10% per year?

The present value of future lump sum = lump sum * present value interest factor

PV                   = 500 * (1.10)-3           = \$ 375.66

##### An individual has \$3,000 today. What will that be worth in 7 years if the going rate of interest is 4% per year?

The future value          =          present value * future value interest factor

Future value of \$ 3,000           =          3000 * (1.04)7

FV                               =          \$ 3,947.80

##### What’s the present value of \$250 received at the end of each year for the next 8 years if the interest rate is 4.5% per year?

Present value of annuity         = annuity * present value annuity factor

PV                   = \$ 250 * [1-(1.045)-8/0.045]   = \$ 1,648

##### References

Clayton, G. E., & Spivey, C. B. (2008). The time value of money: Worked and solved problems. Philadelphia, Pa. [u.a.: Saunders.

Marx, J. (2004). Using financial calculators for time value of money calculations. Cape Town: Pearson/Prentice Hall.

Peterson, D. P., &Fabozzi, F. J. (2009). Foundations and applications of the time value of money. Hoboken, N.J: John Wiley & Sons.