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 11-year annuity of $2,400 per period where payments come at the beginning of each period? The interest rate is 14 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.)
Appendix C Future value of an annuity of $1, FIFA FVA- A 3.278 4.573 3.310 3 4 3.060 3.246 4.375 5.751 6.308 6.975 9.755 10.159 10.583 10.950 11.464 12.006 11.027 11.491 11.978 12.488 13.021 12.578 14.207 13.181 13.816 11.567 12.169 12.808 13.486 12.683 13.412 14.192 15.026 13.809 14.680 15.618 16.627 14.947 15.974 17.086 18.292 16.097 17.293 18.599 20.024 17.258 18.639 20.157 21.825 18.430 20.012 21.762 23.698 19.615 21.412 23.414 25.645 20.811 22.841 25.117 27.671 22.019 24.297 26.870 29.778 28.243 32.030 36.459 41.646 34.785 40.588 47.575 56.085 48.886 60.402 75.401 95.026 1 64.463 84.579 112.80 152.67 16.870 19.599 21.015 23.276 22.550 27.975 30.095 34.405 29.361 23.657 25.840 36.974 41.301 30.840 40.545 33.760 37.379 56.939 20 45.762 57.275 98.347 54.865 47.727 66.439 20.80 154.76 199.64 259.06 337.89 84.701 114.41 199.02 94.461 113.28 442.59 50 1,163.9 Appendix C (concluded) 14 3.539 3.572 3 4 3.440 4.921 3.473 5.066 8.323 9.207 15.073 10.089 10.405 10.730 1.067 12.300 12.757 13.233 13.727 14.776 5.416 16.085 16.786 17.549 18.420 19.337 20.304 20.655 21.814 23.045 24.349 24.133 25.650 27.271 29.002 28.029 29.985 32.089 34.352 32.393 34.883 37.581 40.505 37.280 40.417 43.842 47.580 42.753 46.672 50.980 55.717 48.884 53.739 59.118 65.075 55.750 61.725 68.394 75.836 84.141 93.406 103.74 115.27 128.1 63.440 70.749 78.969 88.212 72.052 80.947 91.025 102.44 15.327 16.499 14.773 18.285 32.015 21.321 22.393 23.521 24.701 25.959 42.566 39.581 48.497 74.327 97.625 32.824 42.219 50.818 60.965 72.939 87.068 45.244 68.760 43.672 72.035 7.442 109.69 138.11 173.64 218.05 273.56 342.95 66.261 167.29 60.925 96.022 05.93 2 98.603 110.29 130.03 138.17 165.42 483.97 20 186.69 249.21 133.33 155.62 181.87 212.79 241.33 293.20 356.79 434.75 767.09 1,013.7 1,342.0 1,779.1 2,360.8 3,134.5 4,163.21 5,529.8 7,343.9 30,089.0 120,393.0 647.44 966.7 1,181.9 40 2,400.0 3,459.5 4,994.5 7,217.710,436.0 15,090.0 21,813.0 31,515.0 45,497.0 280,256.0 1,659,76.0
Explanation / Answer
We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.
HENCE
A=2400(1.14)^11+2400(1.14)^10+2400(1.14)^9+.............+2400(1.14)^1
=$2400[1.14^11+1.14^10+1.14^9+.............+1.14^1]
=$2400*26.27074871
=$63049.80(Aprox)
