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Question 919310: Katy needs to open a holiday savings account to start saving for her holiday in 5 years time. Her bank has a savings account which has an interest rate of 5.4% p.a. compounded quarterly. Katy is paid monthly and so wishes to set-up a direct-debit on her pay-day, which makes a regular monthly deposit into her holiday savings account.
a) How much should her regular monthly deposit be into her holiday savings account, to ensure she has the required funds ($20,000)in 5 years time?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! my assumptions are:
you make direct deposit payments into the account at the end of each month.
the bank pays interest at the end of each quarter for the amount that was deposited in the bank at the end of the previous quarter.
you do not earn any additional interest on any money deposited between each quarter.
based on that assumption, your problem can be translated as follows:
5 years multiplied by 4 equals 20 quarters.
5.4% interest divided by 4 = 1.35% interest earned on your money at the end of each quarter.
you make the same payment at the end of each quarter for 20 quarters.
at the end of the 20 quarters you will have $20,000 in the account.
the quarterly payment required comes out to be equal to $877.77 rounded up to 2 decimal places.
that will get you about 18 cents more than $20,000 at the end of the 20 quarters.
divide that by 3 because there are 3 months in every quarter and you need to put $292.59 in the account at the end of every month.
if you do that, at the end of each quarter you will have deposited an additional $877.77 into the account and the quarterly interest will be applied to the balance at the end of the previous quarter.
the monthly and quarterly accruals will look like this based on my assumptions.
month pmt1 bal1 pmt2 bal2
0 0
1 292.59 292.59
2 292.59 585.18
3 292.59 877.77 877.77 877.77
4 292.59 1170.36
5 292.59 1462.95
6 292.59 1767.389895 877.77 1767.389895
7 292.59 2059.979895
8 292.59 2352.569895
9 292.59 2669.019659 877.77 2669.019659
10 292.59 2961.609659
11 292.59 3254.199659
12 292.59 3582.821424 877.77 3582.821424
13 292.59 3875.411424
14 292.59 4168.001424
15 292.59 4508.959513 877.77 4508.959513
16 292.59 4801.549513
17 292.59 5094.139513
18 292.59 5447.600467 877.77 5447.600467
19 292.59 5740.190467
20 292.59 6032.780467
21 292.59 6398.913073 877.77 6398.913073
22 292.59 6691.503073
23 292.59 6984.093073
24 292.59 7363.068399 877.77 7363.068399
25 292.59 7655.658399
26 292.59 7948.248399
27 292.59 8340.239823 877.77 8340.239823
28 292.59 8632.829823
29 292.59 8925.419823
30 292.59 9330.60306 877.77 9330.60306
31 292.59 9623.19306
32 292.59 9915.78306
33 292.59 10334.3362 877.77 10334.3362
34 292.59 10626.9262
35 292.59 10919.5162
36 292.59 11351.61974 877.77 11351.61974
37 292.59 11644.20974
38 292.59 11936.79974
39 292.59 12382.63661 877.77 12382.63661
40 292.59 12675.22661
41 292.59 12967.81661
42 292.59 13427.5722 877.77 13427.5722
43 292.59 13720.1622
44 292.59 14012.7522
45 292.59 14486.61443 877.77 14486.61443
46 292.59 14779.20443
47 292.59 15071.79443
48 292.59 15559.95372 877.77 15559.95372
49 292.59 15852.54372
50 292.59 16145.13372
51 292.59 16647.7831 877.77 16647.7831
52 292.59 16940.3731
53 292.59 17232.9631
54 292.59 17750.29817 877.77 17750.29817
55 292.59 18042.88817
56 292.59 18335.47817
57 292.59 18867.69719 877.77 18867.69719
58 292.59 19160.28719
59 292.59 19452.87719
60 292.59 20000.1811 877.77 20000.1811
$259.59 is deposited at the end of each month.
interest is accrued quarterly on the balance in the account at the end of the previous quarter.
the end of the previous quarter is the same time point as the beginning of the current quarter.
for example:
time point 0 is the end of the previous quarter and the beginning of the first quarter.
time point 3 is the end of the first quarter and the beginning of the second quarter.
time point 6 is the end of the second quarter and the beginning of the third quarter.
time point 9 is the end of the third quarter and the beginning of the fourth quarter.
time point 12 is the end of the fourth quarter and the beginning of the fifth quarter.
etc...
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