Question

Which of the following annuities has the lowest present value? where applicable, use the same compounding pattern for the deferred years as for the years payments were made.

select one:
a. a series of 8 annual payments of $4,000 paid on the first day of the year for each of the next 8 years (compounded annually) with an interest rate of 9%.
b. a series of payments of $2,250 paid on the last day of each six-month period (compounded semiannually) for 7 years with an interest rate of 9%.
c. no payments made for two years and then the same payment pattern as a.
d. no payments made for one year and then the same payment pattern as b.
e. both a and c are equal and the lowest. f. both b and d are equal and the lowest.

Answer 1

Annuities with deferred payments generally have a lower present value than those with immediate payments because money has a greater value today than it does in the future due to the time value of money.

Step-by-step explanation:

Among annuities with different payment patterns, the present value (PV) of the series of payments considered depends on the timing and amount of each payment in relation to the interest rate. Factors such as deferrals and variances in payment amounts have a direct impact on present value calculations.

Given the options outlined, without specific numerical details, we typically assume that annuities with a deferred start have a lower present value than those with immediate payments because money today is worth more than money tomorrow due to the time value of money.

Therefore, in a general sense, an annuity with no payments made for one year (option d) and then resuming the same payment pattern as another given option would generally result in a lower present value than options with immediate payments.