Calculation formula. Used notations. Project Breakdown.
[1] Calculation method used: 30 / 360
Number of days in a month = 30
Number of days in a year = 360
[2] Future Investment Value, FV
Calculation formula:
FV =
P × (1 + r/n)n×t
FV, Future Investment Value
P, Principal (initial amount), P = 1,066.00
r, Annual compound interest rate, r = 0.05%
n, Number of times the interest compounds during a year
Compound frequency: daily (360 times a year)
n = 360
r/n = 0.05%/360 = (0.05 ÷ 100)/360 = 0.05/(100 × 360)
r/n = 0.000001388889
t, Duration of the investment
n×t, Duration of the investment, related to n
n×t =
+ 5 years × 360 days / year
+ 3 months × 30 days / month
+ 15 days
n×t = 1,905 days
Calculate FV
Substitute for the values in the FV formula:
FV =
P × (1 + r/n)n×t =
1,066.00 × (1 + 0.000001388889)1,905 =
1,066.00 × 1.0000013888891,905 =
1,066.00 × 1.002649335009 ≈
1,068.82
[3] Compound interest amount, CI
Calculation formula
CI = FV - P
CI, compound interest amount
FV, Future Investment Value
P, Principal (initial amount)
CI ≈
1,068.82 - 1,066.00 ≈
2.82
[4] Project Breakdown. Monthly.
Interest compounded: daily (360 times a year).
Month | Days | Interest | Total interest | Balance |
---|
0 | 0 | -- | -- | 1,066.00 |
1 | 30 | 0.04 | 0.04 | 1,066.04 |
2 | 30 | 0.04 | 0.09 | 1,066.09 |
3 | 30 | 0.04 | 0.13 | 1,066.13 |
4 | 30 | 0.04 | 0.18 | 1,066.18 |
5 | 30 | 0.04 | 0.22 | 1,066.22 |
6 | 30 | 0.04 | 0.27 | 1,066.27 |
7 | 30 | 0.04 | 0.31 | 1,066.31 |
8 | 30 | 0.04 | 0.36 | 1,066.36 |
9 | 30 | 0.04 | 0.40 | 1,066.40 |
10 | 30 | 0.04 | 0.44 | 1,066.44 |
11 | 30 | 0.04 | 0.49 | 1,066.49 |
12 | 30 | 0.04 | 0.53 | 1,066.53 |
13 | 30 | 0.04 | 0.58 | 1,066.58 |
14 | 30 | 0.04 | 0.62 | 1,066.62 |
15 | 30 | 0.04 | 0.67 | 1,066.67 |
16 | 30 | 0.04 | 0.71 | 1,066.71 |
17 | 30 | 0.04 | 0.76 | 1,066.76 |
18 | 30 | 0.04 | 0.80 | 1,066.80 |
19 | 30 | 0.04 | 0.84 | 1,066.84 |
20 | 30 | 0.04 | 0.89 | 1,066.89 |
21 | 30 | 0.04 | 0.93 | 1,066.93 |
22 | 30 | 0.04 | 0.98 | 1,066.98 |
23 | 30 | 0.04 | 1.02 | 1,067.02 |
24 | 30 | 0.04 | 1.07 | 1,067.07 |
25 | 30 | 0.04 | 1.11 | 1,067.11 |
26 | 30 | 0.04 | 1.16 | 1,067.16 |
27 | 30 | 0.04 | 1.20 | 1,067.20 |
28 | 30 | 0.04 | 1.24 | 1,067.24 |
29 | 30 | 0.04 | 1.29 | 1,067.29 |
30 | 30 | 0.04 | 1.33 | 1,067.33 |
31 | 30 | 0.04 | 1.38 | 1,067.38 |
32 | 30 | 0.04 | 1.42 | 1,067.42 |
33 | 30 | 0.04 | 1.47 | 1,067.47 |
34 | 30 | 0.04 | 1.51 | 1,067.51 |
35 | 30 | 0.04 | 1.56 | 1,067.56 |
36 | 30 | 0.04 | 1.60 | 1,067.60 |
37 | 30 | 0.04 | 1.64 | 1,067.64 |
38 | 30 | 0.04 | 1.69 | 1,067.69 |
39 | 30 | 0.04 | 1.73 | 1,067.73 |
40 | 30 | 0.04 | 1.78 | 1,067.78 |
41 | 30 | 0.04 | 1.82 | 1,067.82 |
42 | 30 | 0.04 | 1.87 | 1,067.87 |
43 | 30 | 0.04 | 1.91 | 1,067.91 |
44 | 30 | 0.04 | 1.96 | 1,067.96 |
45 | 30 | 0.04 | 2.00 | 1,068.00 |
46 | 30 | 0.04 | 2.05 | 1,068.05 |
47 | 30 | 0.04 | 2.09 | 1,068.09 |
48 | 30 | 0.04 | 2.13 | 1,068.13 |
49 | 30 | 0.04 | 2.18 | 1,068.18 |
50 | 30 | 0.04 | 2.22 | 1,068.22 |
51 | 30 | 0.04 | 2.27 | 1,068.27 |
52 | 30 | 0.04 | 2.31 | 1,068.31 |
53 | 30 | 0.04 | 2.36 | 1,068.36 |
54 | 30 | 0.04 | 2.40 | 1,068.40 |
55 | 30 | 0.04 | 2.45 | 1,068.45 |
56 | 30 | 0.04 | 2.49 | 1,068.49 |
57 | 30 | 0.04 | 2.53 | 1,068.53 |
58 | 30 | 0.04 | 2.58 | 1,068.58 |
59 | 30 | 0.04 | 2.62 | 1,068.62 |
60 | 30 | 0.04 | 2.67 | 1,068.67 |
61 | 30 | 0.04 | 2.71 | 1,068.71 |
62 | 30 | 0.04 | 2.76 | 1,068.76 |
63 | 30 | 0.04 | 2.80 | 1,068.80 |
64 | 15 | 0.02 | 2.82 | 1,068.82 |
Month | Days | Interest | Total interest | Balance |
Withdrawal Fee Amount, Fw. Financial gain, Pr
[5] The amount charged for withdrawing the money
Fw = Fw% × FV
Fw, Withdrawal Fee Amount
Fw%, Commission Fee % (on withdrawal), as a percentage
FV, Future Investment Value
Fw =
Fw% × FV =
1% × 1,068.82 =
1/100 × 1,068.82 =
(1 × 1,068.82)/100 =
1,068.82/100 =
1,068.82 ÷ 100 =
10.6882 ≈
10.69
[6] Financial gain, Pr:
Pr = CI - Fw
Pr, financial gain
CI, compound interest amount
Fw, Withdrawal Fee Amount
Pr =
CI - Fw =
2.82 - 10.69 =
- 7.87
Answer:
Principal (initial amount) = 1,066.00
Future Investment Value = 1,068.82
Compound interest amount = 2.82
Withdrawal Fee Amount = 10.69
Financial gain = - 7.87