Question 1039459: In order to accumulate enough money for a down payment on a house, a couple deposits
$ 513 per month into an account paying 3% compounded monthly. If payments are made at the end of each period, how much money will be in the account in 6 years?
Found 2 solutions by Aldorozos, MathTherapy:
Answer by Aldorozos(172)   (Show Source):
You can put this solution on YOUR website!
interest rate
% (r) annually
monthly
number of years
(n)
payment frequency (k) annually semiannually
quarterly monthly
payment amount
(PMT)
payment due at
beginning end of period
present value
(PV)
6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
Please see below to understand the concept of future value of equal payments:
https://www.google.com/search?q=future+value+of+payments+formula&biw=1280&bih=705&tbm=isch&tbo=u&source=univ&sa=X&sqi=2&ved=0ahUKEwiYpd6J1snNAhWBYyYKHWjXAYMQsAQISg
Once you get some ideas go to this site if you don't want to do the calculation:
Use this site:
http://keisan.casio.com/exec/system/1234231998
3% is annually. Number of years is 6 but compounded monthly.
No. year future value interest effective rate
1 513 0 0%
2 1,027.28 1.28 0.125%
3 1,542.85 3.85 0.25%
4 2,059.71 7.71 0.376%
5 2,577.86 12.86 0.501%
6 3,097.3 19.3 0.627%
7 3,618.04 27.04 0.753%
8 4,140.09 36.09 0.879%
9 4,663.44 46.44 1.006%
10 5,188.1 58.1 1.133%
11 5,714.07 71.07 1.259%
12 1 6,241.35 85.35 1.387%
13 6,769.96 100.96 1.514%
14 7,299.88 117.88 1.641%
15 7,831.13 136.13 1.769%
16 8,363.71 155.71 1.897%
17 8,897.62 176.62 2.025%
18 9,432.86 198.86 2.154%
19 9,969.45 222.45 2.282%
20 10,507.37 247.37 2.411%
21 11,046.64 273.64 2.54%
22 11,587.25 301.25 2.669%
23 12,129.22 330.22 2.799%
24 2 12,672.55 360.55 2.928%
25 13,217.23 392.23 3.058%
26 13,763.27 425.27 3.188%
27 14,310.68 459.68 3.319%
28 14,859.45 495.45 3.449%
29 15,409.6 532.6 3.58%
30 15,961.13 571.13 3.711%
31 16,514.03 611.03 3.842%
32 17,068.32 652.32 3.974%
33 17,623.99 694.99 4.105%
34 18,181.05 739.05 4.237%
35 18,739.5 784.5 4.369%
36 3 19,299.35 831.35 4.502%
37 19,860.6 879.6 4.634%
38 20,423.25 929.25 4.767%
39 20,987.31 980.31 4.9%
40 21,552.77 1,032.77 5.033%
41 22,119.66 1,086.66 5.166%
42 22,687.95 1,141.95 5.3%
43 23,257.67 1,198.67 5.434%
44 23,828.82 1,256.82 5.568%
45 24,401.39 1,316.39 5.702%
46 24,975.39 1,377.39 5.837%
47 25,550.83 1,439.83 5.972%
48 4 26,127.71 1,503.71 6.107%
49 26,706.03 1,569.03 6.242%
50 27,285.79 1,635.79 6.377%
51 27,867.01 1,704.01 6.513%
52 28,449.68 1,773.68 6.649%
53 29,033.8 1,844.8 6.785%
54 29,619.38 1,917.38 6.921%
55 30,206.43 1,991.43 7.058%
56 30,794.95 2,066.95 7.195%
57 31,384.94 2,143.94 7.332%
58 31,976.4 2,222.4 7.469%
59 32,569.34 2,302.34 7.607%
60 5 33,163.76 2,383.76 7.745%
61 33,759.67 2,466.67 7.883%
62 34,357.07 2,551.07 8.021%
63 34,955.96 2,636.96 8.159%
64 35,556.35 2,724.35 8.298%
65 36,158.25 2,813.25 8.437%
66 36,761.64 2,903.64 8.576%
67 37,366.55 2,995.55 8.715%
68 37,972.96 3,088.96 8.855%
69 38,580.89 3,183.89 8.995%
70 39,190.35 3,280.35 9.135%
71 39,801.32 3,378.32 9.275%
72 6 40,413.83 3,477.83 9.416
Answer by MathTherapy(10549)  (Show Source):
You can put this solution on YOUR website!
In order to accumulate enough money for a down payment on a house, a couple deposits
$ 513 per month into an account paying 3% compounded monthly. If payments are made at the end of each period, how much money will be in the account in 6 years?
The formula for the future value of an ORDINARY ANNUITY should be used, which is: , where:
 is the future value in the amount of time (years), or the amount that will be available then (UNKNOWN, in this case)
PMT is the payment amount ($513, in this case)
i is the interest rate, per year (3%, or .03, in this case)
m is the number of compounding periods per year (monthly, or 12 in this case)
t is the amount of time, in years, the money is invested (6, in this case)
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