Question

A 30-year annuity has end-of-month payments. The first year the payments are $120 each. In subsequent years the monthly payment increases by $5 over what it was the previous year.

Find the accumulated value of this annuity if AEIR=3%

	A.	105,070
	B.	100,620
	C.	41,560
	D.	84,820
	E.	42,390

Answer 1

Solution- We have the first year payments as $120 per year and it increases ($5 per month). n ie., 5x12 per yecov = $60. 1ѣexeko90 , first year = $120. second year payment = $120+$60. ke kill first find the present value of the annuity payments as follows. It feest payment = p. second payment = ptQ. and ++ payment = (p-+ Qt. The present value of this annuity payment = (p-Qan + Q (Ian. here, p=120 ; Q = 60; n = 30. = 120-60) a 30 + 60 (Ia) 30 = 60 a 30 + 60 (10) 30). Now, v 20.03 ve Yi+y = 71.03.

a 37 - I-W30 = 1- (0.970874) 0.03 19.6004 a 301 - (Ia) = a - DV = I-V 1- (0.9708+4) - Whore, ? - Yuty = 0.031.03 = 0.029126. 30 ani, 1-10.970874)30 0.029126 azol 20.18850928, (la)301 = 20.18850928 - (30)(0.970874) 30 0.03 (Ia) 301 - 260.9617. is present Value = 601 230 +(1a)301 ] = 60(19.6004+260.9674) = 601280.5621) px - $16833.726.

conta Accumulated value, = 16833.726 ( 1+Vj 30 = 16833. 726 (1.03) 30 = $40859.87137. Hence, the closest value = $41560. This is due to round of values.. Therefore, option -(C) $41,560 is correct ansklerin