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 |
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