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 = 5.00%
n - Number of times the interest compounds during a year
Compound frequency: annually (once a year)
n = 1
r/n = 5.00%/1 = (5.00 ÷ 100)/1 = 5.00/(100 × 1)
r/n = 0.05
Duration of the investment. Number of compounding periods
[4] Duration of the investment, t
t = 2 years and 29 days
The investment duration period, in days:
+ 2 years × 360 days / year
+ 29 days
t = 749 days
[5] Number of compounding periods
Interest compounded: annually (once a year).
Compounding period duration, dcp, is:
360 ÷ 1 = 360 days (one year).
Number of compounding periods:
t ÷ dcp = 749 ÷ 360 = 2 + remainder 29
There are 2 full compounding periods.
+ Plus a partial compounding period, of 29 days.
There are 3 compounding periods in total.
Calculation: Future Investment Value. Compound Interest
[6] Project Breakdown.
Step-by-step explanations
Interest compounded: annually
Contribution frequency: every two weeks
(26 times a year, every 14 days)
Contribution added to the balance:
at the end of each compounding period
There are 3 compounding periods in total.
Below, the calculations for each period.
Start year 1.
Duration: 360 days = a full compounding period.
Calculate the Future Investment Value
at the end of the compounding period:
1.00 × (1 + 0.05)1 =
1.00 × 1.05 =
1.05
Add the periodic contributions to the balance:
1.05 + 25 × 2.00 =
1.05 + 50.00 =
51.05
Start year 2.
Duration: 360 days = a full compounding period.
Calculate the Future Investment Value
at the end of the compounding period:
51.05 × (1 + 0.05)1 =
51.05 × 1.05 =
53.60
Add the periodic contributions to the balance:
53.60 + 26 × 2.00 =
53.60 + 52.00 =
105.60
Start year 3.
Duration: 29 days = a partial compounding period.
Calculate the Future Investment Value
at the end of the compounding period:
105.60 × (1 + 0.05)(29 ÷ 360) =
105.60 × (1 + 0.05)0.080555555556 =
105.60 × 1.003938052612 =
106.02
Add the periodic contribution to the balance:
106.02 + 2 × 2.00 =
106.02 + 4.00 =
110.02
[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 =
110.02 - (1.00 + 106.00) =
110.02 - 107.00 =
3.02
Answer: