Question

Annuity payments are assumed to come at the end of each payment period (termed an ordinary annuity). However, an exception occurs when the annuity payments come at the beginning of each period (termed an annuity due). What is the future value of a 18-year annuity of $2,000 per period where payments come at the beginning of each period? The interest rate is 5 percent. Use Appendix C for an approximate answer, but calculate your final answer using the formula and financial calculator methods. To find the future value of an annuity due when using the Appendix tables, add 1 to n and subtract 1 from the tabular value. For example, to find the future value of a $100 payment at the beginning of each period for five periods at 10 percent, go to Appendix C for n = 6 and i = 10 percent. Look up the value of 7.716 and subtract 1 from it for an answer of 6.716 or $671.60 ($100 × 6.716). (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Answer 1

Answer:

The future value of a 18-year annuity of $2,000 per period where payments come at the beginning of each period is $59,078.

Explanation:

We apply the formula to calculate future value of annuity to find the future value of 18-year annuity as at the beginning of year 18 ( because payment comes at the beginning of the year):

2,000/5% x (1.05^18 -1) = $56,264.77.

We further compound the future value of 18-year annuity as at the beginning of year 18 for one period to come up with the future value of this annuity as at the end of 18 year time:

56,264.77 x 1.05 = $59,078.

So, the answer is $59,078.