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 13-year annuity of $3,500 per period where payments come at the beginning of each period? The interest rate is 10 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

Formula method:

We are given the following information:

Annual payment	PMT	$            3,500.00
rate of interest	r	10.00%
number of years	n	13
Future value	FV	To be calculated

We need to solve the following equation to arrive at the required FV

So the FV of the beginning annuity is $94412.44

Financial calcualtor Method:

First put it in the BGN mode and then input N=13, I/Y= 10,PMT = 3500, PV = 0 CPT FV

If you can't put in the BGN mode then input the same values and multiply the arrived FV by (1+r) because the FV of a beginning annutiy is nothing but FV of ending annuity x (1+r) as CFs are compounded for one extra period.