Question

Carl and Cassia need to replace a delivery van in 3 years. The cost of delivery vans is $23,000 today, and is expected to grow 5% a year over the next 3 years. If Carl and Cassia have saved $4,500 towards the van already, how much per month do Carl and Cassia need to save, if they think they can earn 7% per year on their savings, to pay for the new van 3 years from now?

		$528
		$805
		$185
		$178
		$223

Answer 1

Current Price of VAN	23000
(A) Price at the end of 3rd year	26625	23000*(1.05)^3
Current Saving	4500
(B) Fund Value at the end of 3rd year	5513	4500*(1.07)^3
(A-B) Balance Money needed at the end of 3rd year (FV)	21113	(26625-5513)
This is the amount Carl and Cassia need at the end of 3rd yeat to in additon to their current saving at the end of 3rd year. So this can be assumed as a FV at the end of 3rd year.
As we need to calculate the monthly saving (which earn 7% pa) as required by Carl and Cassia to accumulate the $21113 at the end of 3rd year.
We can solve this with the help of FV of ordiniary annuity formula
FV of Ordiniary Annuity =	Monthly Saving *		{(1+r)^n-1}
			r
r =	0.583%	(7%/12)
n =	36	(12*3)
Monthly Saving =	21112.6815*	0.5833%
		{(1+.5833%)^36-1}
Monthly Saving =	528.741
Months	Opening	Monthly Saving (end of month)	Interest on Monthly Saving	Closing Balance
1	0	528.741003	0	528.741
2	528.741003	528.741003	3.08432252	1060.566
3	1060.566329	528.741003	6.18663692	1595.494
4	1595.493968	528.741003	9.30704815	2133.542
5	2133.54202	528.741003	12.4456618	2674.729
6	2674.728684	528.741003	15.602584	3219.072
7	3219.072271	528.741003	18.7779216	3766.591
8	3766.591196	528.741003	21.971782	4317.304
9	4317.303981	528.741003	25.1842732	4871.229
10	4871.229257	528.741003	28.415504	5428.386
11	5428.385764	528.741003	31.6655836	5988.792
12	5988.792351	528.741003	34.934622	6552.468
13	6552.467976	528.741003	38.2227299	7119.432
14	7119.431709	528.741003	41.5300183	7689.703
15	7689.70273	528.741003	44.8565993	8263.3
16	8263.300332	528.741003	48.2025853	8840.244
17	8840.243921	528.741003	51.5680895	9420.553
18	9420.553013	528.741003	54.9532259	10004.25
19	10004.24724	528.741003	58.3581089	10591.35
20	10591.34635	528.741003	61.7828537	11181.87
21	11181.87021	528.741003	65.2275762	11775.84
22	11775.83879	528.741003	68.6923929	12373.27
23	12373.27219	528.741003	72.1774211	12974.19
24	12974.19061	528.741003	75.6827786	13578.61
25	13578.61439	528.741003	79.208584	14186.56
26	14186.56398	528.741003	82.7549565	14798.06
27	14798.05994	528.741003	86.3220163	15413.12
28	15413.12296	528.741003	89.9098839	16031.77
29	16031.77384	528.741003	93.5186808	16654.03
30	16654.03353	528.741003	97.1485289	17279.92
31	17279.92306	528.741003	100.799551	17909.46
32	17909.46361	528.741003	104.471871	18542.68
33	18542.67649	528.741003	108.165613	19179.58
34	19179.5831	528.741003	111.880901	19820.21
35	19820.20501	528.741003	115.617863	20464.56
36	20464.56387	528.741003	119.376623	21112.68