Question

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.

Answer 1

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