Question

When finding the future value (FV7) of a deferred annuity of five annual payments of \$1000,...

When finding the future value (FV7) of a deferred annuity of five annual payments of \$1000, with the first payment at the beginning of year four, which of the following is correct? The relevant rate 10% pa. a.FV7 = 1000 x FVIFA(5,.1) b.FV7 = 1000 x FVIFA(5,.1) x (1.1)-1 c.FV7 = 1000 + 1000 x (1.1) + 1000 x (1.1)2 + 1000 x (1.1)3 + 1000 x (1.1)4 d.Both (a) and (c) are correct. e.FV7 = 1000 x FVIFA(7,.1). I dont quite understand the answer, as the correct answer is (D). Isn't it 1000[ (1+0.1)^8-1/0.1] - 1000[1+0.1)^3/0.1 The explanation ive given above is by using 8 annuities (due to deferred) and deduct those years that is being deferred, would appreciate if you can provide information based on this. Thanks.

 1) The payments are made at t3, t4, t5, t6 and t7 and the FV is at t7. One of the options is simply the FV of annuity of \$1000 for 5 years which, using the interest factor = 1000*FVIFA(10%,5). Using the formula it would be 1000*(1.1^5-1)/(0.1*1.1^5). The second option is to find the FV of each of the payments and taking the sum which would be = 1000+1000*1.1+1000*1.1^2+1000*1.1^3+1000*1.1^4 = \$        6,105.10 Hence, the correct answer is D. 2) As for the calculation suggested by you: There are only 7 years not 8, the payments being t3 to t7. Your formula should be = 1000*(1.1^7-1)/0.1-((1000*(1.1^2-1)/0.1))*1.1^5 = \$        6,105.10