Question

An annuity pays quarterly for 16 years at the beginning of each quarter. Payments during the first year are 250/quarter. Year 2 payments are each 105. The payments go up by 150 for each subsequent year but are level within each year. AEIR = 5%, please find the accumulated value of this annuity just prior to the payment at t=15.

Please show all steps, I don't need graphs so do not use excel, I need steps.

	A.	79,798.78
	B.	The answer does not appear here
	C.	72,848.29
	D.	154,014.68
	E.	156,104.12

Answer 1

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Cheers!!!

I have solved this question previously. I am attaching the steps to be followed for solving this problem.

Also, for calculation of steps in payments for around 60 times, I think it is inherent to use excel for calcualtion as well as display purposes.

Initially we try to calcuate the rate of interest which is given by

r = (1 + AEIR)^{(PAYMENT FREQUENCY)}

r = (1+ 5%)^1/4

r ⁼ 1.2272234%

Next we calculate the annuity for each payment time period using the following table where

FV = Cash flows ( 1 +r)ⁿ

Here cash flows are 250 and 105 for first 8 quarters and are stepped up by 150 in the payments after the 8th Quarter.

At t= 15 ( 15*4) = 60 Payments, we get the following table,

Time = t (60 - t) Cash flows Future Value 250 60 519.7320316 250 513.4310852 59 58 250 507.206528 3 57 250 501.0574339 56 105 4 207.892813 205.3724344 105 55 54 6. 105 202.8826116 53 105 200.4229739 255 52 480.8405207 475.0110736 51 255 50 10 255 469.2522996 463.5633418 11 49 255 405 727.3217972 718.5041462 48 12 47 13 405 405 14 46 709.7933956 701.1882493 15 45 405 2.

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48 1755 12 2031.631865 2007.001473 1982.669687 49 11 1755 10 50 1755 1958.632886 51 1755 52 2100.262493 1905 53 1905 2074.800061 2049.646322 54 1905 2024.797533 55 1905 2157.749996 2055 56 41 2131.590617 57 2055 58 2055 2105.748381 59 2055 2080.219441 Total 79798.776

We find that option A is the answer.

Cheers!!!!