Question

How do I work this problem?

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 $3,000 per period where payments come at the beginning of each period? The interest rate is 11 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

period of investment, n = 13

annuity amount, A = $3000

interest rate, r = 11% = 0.11

here , n = 14

according to the question , we will add 1 to value of period of investment

i = 11%

then we will look for the value in Appendix C for i = 11% and n = 14

this will be equal to FVIFA = [(1+r)ⁿ -1]/r = [(1.11)¹⁴-1]/0.11 = 30.095

then we will subtract 1 from FVIFA

we will get an amount = 30.095 - 1 = 29.095

future value = 3000*29.095 = $87284.75

this is an approximate value of the future value

accrding to formula

FVIFA = [(1+r)ⁿ -1]/r = [(1.11)¹³ - 1]/0.11 = 26.2116378

Future value = A*FVIFA*(1+r) = 3000*26.2116378*1.11 = $87284.754 Or $87284.75