Calculate the Future Investment Value and the Compound Interest earned by a principal of 139.00 (Dollar, Euro, Pound, ...), initial amount of money lent, deposited or borrowed, with a duration of 5 years, 11 months and 27 days, 10.00% annual interest rate, compounded daily (360 times a year) with a regular contribution of 46.00, monthly made (12 times a year), added to the balance at the beginning of each compounding period

Calculation method used. Calculation formula. Used notations.


[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:

For a full compounding period:


FV = P × (1 + r/n)1


For a partial compounding period:


FV = P × (1 + r/n)(np ÷ nt)


np - number of days in the partial period

nt - number of days in the full period


[3] Used notations:

FV - Future Investment Value


P - Balance at the beginning of the compounding period


r - Annual compound interest rate, r = 10.00%


n - Number of times the interest compounds during a year
Compound frequency: daily (360 times a year)
n = 360


r/n = 10.00%/360 = (10.00 ÷ 100)/360 = 10.00/(100 × 360)
r/n = 0.000277777778


>> Compound Interest: what is it, how is it calculated?


Duration of the investment. Number of compounding periods

[4] Duration of the investment, t

t = 5 years, 11 months and 27 days


The investment duration period, in days:

+ 5 years × 360 days / year
+ 11 months × 30 days / month
+ 27 days

t = 2,157 days


[5] Number of compounding periods

Interest compounded: daily (360 times a year).


Compounding period duration, dcp, is:

360 ÷ 360 = 1 day (one day).


Number of compounding periods:

t ÷ dcp = 2,157 ÷ 1 = 2,157


There are 2,157 compounding periods in total.


Calculation: Future Investment Value. Compound Interest

[6] Project Breakdown.

Step-by-step explanations

Interest compounded: daily


Contribution frequency: monthly

(12 times a year, every 30 days)


Contribution added to the balance:
at the beginning of each compounding period


There are 2,157 compounding periods in total.

Below, the calculations for some of them.


The first three compounding periods:

Start day 1.


Add the periodic contribution to the balance:

139.00 + 46.00 =

185.00


Calculate the Future Investment Value
at the end of the compounding period:

185.00 × (1 + 0.000277777778)1 =

185.00 × 1.000277777778 =

185.05


Start day 2.


Calculate the Future Investment Value
at the end of the compounding period:

185.05 × (1 + 0.000277777778)1 =

185.05 × 1.000277777778 =

185.10


Start day 3.


Calculate the Future Investment Value
at the end of the compounding period:

185.10 × (1 + 0.000277777778)1 =

185.10 × 1.000277777778 =

185.15


And the process goes along,
as detailed in the steps above.


An intermediate compounding period,
regular contribution added to the balance:

Start day 31.


Add the periodic contribution to the balance:

186.55 + 46.00 =

232.55


Calculate the Future Investment Value
at the end of the compounding period:

232.55 × (1 + 0.000277777778)1 =

232.55 × 1.000277777778 =

232.61


The last two compounding periods:

Start day 2,156.


Calculate the Future Investment Value
at the end of the compounding period:

4,803.40 × (1 + 0.000277777778)1 =

4,803.40 × 1.000277777778 =

4,804.73


Start day 2,157.


Calculate the Future Investment Value
at the end of the compounding period:

4,804.73 × (1 + 0.000277777778)1 =

4,804.73 × 1.000277777778 =

4,806.07


[7] Project Summary. Monthly

Interest compounded: daily


Contribution frequency: monthly


Contribution added to the balance:
at the beginning of each compounding period


Month Days Deposits Total
deposits
Interest Total
interest
Balance
0 -- 139.00 139.00 -- -- 139.00
1 30 46.00 185.00 1.55 1.55 186.55
2 30 46.00 231.00 1.95 3.49 234.49
3 30 46.00 277.00 2.35 5.84 282.84
4 30 46.00 323.00 2.75 8.59 331.59
5 30 46.00 369.00 3.16 11.75 380.75
6 30 46.00 415.00 3.57 15.32 430.32
7 30 46.00 461.00 3.99 19.31 480.31
8 30 46.00 507.00 4.40 23.71 530.71
9 30 46.00 553.00 4.83 28.54 581.54
10 30 46.00 599.00 5.25 33.79 632.79
11 30 46.00 645.00 5.68 39.47 684.47
12 30 46.00 691.00 6.11 45.58 736.58
13 30 46.00 737.00 6.55 52.13 789.13
14 30 46.00 783.00 6.99 59.11 842.11
15 30 46.00 829.00 7.43 66.54 895.54
16 30 46.00 875.00 7.88 74.42 949.42
17 30 46.00 921.00 8.33 82.75 1,003.75
18 30 46.00 967.00 8.78 91.53 1,058.53
19 30 46.00 1,013.00 9.24 100.78 1,113.78
20 30 46.00 1,059.00 9.70 110.48 1,169.48
21 30 46.00 1,105.00 10.17 120.65 1,225.65
22 30 46.00 1,151.00 10.64 131.29 1,282.29
23 30 46.00 1,197.00 11.11 142.40 1,339.40
24 30 46.00 1,243.00 11.59 153.99 1,396.99
25 30 46.00 1,289.00 12.07 166.07 1,455.07
26 30 46.00 1,335.00 12.56 178.63 1,513.63
27 30 46.00 1,381.00 13.05 191.68 1,572.68
28 30 46.00 1,427.00 13.54 205.22 1,632.22
29 30 46.00 1,473.00 14.04 219.26 1,692.26
30 30 46.00 1,519.00 14.54 233.81 1,752.81
31 30 46.00 1,565.00 15.05 248.86 1,813.86
32 30 46.00 1,611.00 15.56 264.42 1,875.42
33 30 46.00 1,657.00 16.08 280.49 1,937.49
34 30 46.00 1,703.00 16.60 297.09 2,000.09
35 30 46.00 1,749.00 17.12 314.21 2,063.21
36 30 46.00 1,795.00 17.65 331.86 2,126.86
37 30 46.00 1,841.00 18.18 350.04 2,191.04
38 30 46.00 1,887.00 18.72 368.76 2,255.76
39 30 46.00 1,933.00 19.26 388.01 2,321.01
40 30 46.00 1,979.00 19.80 407.82 2,386.82
41 30 46.00 2,025.00 20.36 428.17 2,453.17
42 30 46.00 2,071.00 20.91 449.08 2,520.08
43 30 46.00 2,117.00 21.47 470.55 2,587.55
44 30 46.00 2,163.00 22.03 492.59 2,655.59
45 30 46.00 2,209.00 22.60 515.19 2,724.19
46 30 46.00 2,255.00 23.18 538.37 2,793.37
47 30 46.00 2,301.00 23.76 562.13 2,863.13
48 30 46.00 2,347.00 24.34 586.47 2,933.47
49 30 46.00 2,393.00 24.93 611.40 3,004.40
50 30 46.00 2,439.00 25.52 636.92 3,075.92
51 30 46.00 2,485.00 26.12 663.04 3,148.04
52 30 46.00 2,531.00 26.72 689.77 3,220.77
53 30 46.00 2,577.00 27.33 717.10 3,294.10
54 30 46.00 2,623.00 27.95 745.05 3,368.05
55 30 46.00 2,669.00 28.57 773.61 3,442.61
56 30 46.00 2,715.00 29.19 802.80 3,517.80
57 30 46.00 2,761.00 29.82 832.62 3,593.62
58 30 46.00 2,807.00 30.45 863.07 3,670.07
59 30 46.00 2,853.00 31.09 894.16 3,747.16
60 30 46.00 2,899.00 31.74 925.90 3,824.90
61 30 46.00 2,945.00 32.39 958.29 3,903.29
62 30 46.00 2,991.00 33.04 991.33 3,982.33
63 30 46.00 3,037.00 33.71 1,025.04 4,062.04
64 30 46.00 3,083.00 34.37 1,059.41 4,142.41
65 30 46.00 3,129.00 35.04 1,094.45 4,223.45
66 30 46.00 3,175.00 35.72 1,130.18 4,305.18
67 30 46.00 3,221.00 36.41 1,166.58 4,387.58
68 30 46.00 3,267.00 37.10 1,203.68 4,470.68
69 30 46.00 3,313.00 37.79 1,241.47 4,554.47
70 30 46.00 3,359.00 38.49 1,279.96 4,638.96
71 30 46.00 3,405.00 39.20 1,319.16 4,724.16
72 27 46.00 3,451.00 35.91 1,355.07 4,806.07
Month Days Deposits Total
deposits
Interest Total
interest
Balance

[8] Compound interest amount, CI

Calculation formula:


CI = FV - (P + Tot. Contrib.)


CI - compound interest amount

FV - Future Investment Value

P - Principal (initial amount)

Tot. Contrib. - Total value of contributions


Calculate the compound interest amount:


CI =


4,806.07 - (139.00 + 3,312.00) =


4,806.07 - 3,451.00 =


1,355.07


Answer:

Principal (initial amount) = 139.00

Deposits = 3,312.00

Principal + Deposits = 3,451.00


Future Investment Value = 4,806.07

Compound interest amount = 1,355.07


More operations of this kind:

Calculator: Compound Interest, Future Investment Value

FV = P × (1 + r/n)n×t + A × [(1 + r/m)m×t - 1] ÷ r/m

FV = Future Value of investment

P = Principal amount invested (the original contribution)

A = Regular contribution (additional money added periodically to the initial investment, P)

r = Annual Interest Rate the investment is earning

n = Number of times the interest compounds during a year

m = Number of times the regular contribution is made during a year

t = Number of years the investment is going to be active

t and r are expressed using the same time units

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