Q1. How Does the Present Value of A Lump Sum Compare To The Present Value Of An Annuity?

The present value of an annuity refers to the sum which must be invested at the present to guarantee the desired amount of payment at some time in the future while the present value of a lump sum refers to the amount of payment that would be transacted at a given time in the future is worth today (Marx, 2009). The two values differs as the present value of a lump sum attempts to ascertain the worth of a given proposed investment at the current moment whereas the present value of an annuity is the amount that should be spent to obtain a given return in the future (Marx, 2009).

Q2. How Does the Future Value of An Ordinary Annuity Compare to the Future Value Of An Annuity Due?

An ordinary annuity refers to a series of payments that are made over a given period of time. It is characterized by having all the payments being made using similar amounts, made within same time interval and at every end of the period (Marx, 2009). On the other hand, the future value of an annuity due refers to payments that are made repeatedly at the beginning of every period and contains the features like having payments of similar amounts, payments made at similar intervals and made at the beginning of each period. In this regard, an annuity due exhibits a higher future value compared to the ordinary annuity because payments are made at the beginning of the period for the latter (Marx, 2009).

Q3. How Does the Present Value of An Annuity Compare to the Present Value of An Annuity Due?

The present value of an annuity refers to the amount of a series of payments that are to be paid at a given periodic time in the future. Particularly, the value shows the amount of periodic cash flows that are expected to be made in the future at a particular discount rate or rate of returns. Since the future cash flow of the annuity is discounted at a given discount rate, the amount is higher when the discount rate is low and low when the discount rate is higher (Marx, 2009). On the other hand, the present value of annuity due refers to a set of payments that should be made at the present or at the immediate time (Marx, 2009).

Q4. Whats The Value Today Of $500 Received in 3 Years If the Going Rate of Interest Is 10% Per Year?

To obtain the present value of $500 received in 3 years at the rate of 10% per year, the present value of a lump sum as follows:

PV=FV1+InWhereby:

PV = Present value

FV = Future value

I = interest rate

N = number of the compounding periods

Hence, PV = $500.00 * (1 + 10%) ^-3 = $375.657. Here, it implies that the value of $500 in three years time at 10% interest rate today is $375.657.

Q5. An Individual Has $3,000 Today. What Will That Be Worth In 7 Years If The Going Rate Of Interest Is 4% Per Year?

Using future value of a lump sum formula, the following is the worth of $3000 7 years from now at a 4% interest rate per year.

FV=PV*1+rnWhereby;

FV = Future value

PV = Present value

R = Interest rate to be paid

N = Number of years.

FV = $3,000*(1+0.04) ^7 = $3,947.795.

Q6. Whats 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?

Using the present value of an annuity due formula, the present value is as follows:

PV=P+P{1-1+r-n-1r}Whereby:

P=periodic payment

N = number of periods

R=rate per period

Hence, PV = $250.0 + $250.0*{1-(1+0.045)^-(8-1))/0.045} = $1,723.175.

References

Marx, J. (2009). Financial management in Southern Africa. Cape Town South Africa: Pearson Education South Africa.

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