Duration of the investment. Number of compounding periods
[4] Duration of the investment, t
t = 5 years, 5 months and 4 days
The investment duration period, in days:
+ 5 years × 360 days / year
+ 5 months × 30 days / month
+ 4 days
t = 1,954 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 = 1,954 ÷ 360 = 5 + remainder 154
There are 5 full compounding periods.
+ Plus a partial compounding period, of 154 days.
There are 6 compounding periods in total.
Calculation: Future Investment Value. Compound Interest
[6] Project Breakdown.
Step-by-step explanations
Interest compounded: annually
Contribution frequency: monthly
(12 times a year, every 30 days)
Contribution added to the balance:
at the beginning of each compounding period
There are 6 compounding periods in total.
Below, the calculations for some of them.
The first three compounding periods:
Start year 1.
Duration: 360 days = a full compounding period.
Add the periodic contributions to the balance:
10,982.00 + 12 × 1,984.00 =
10,982.00 + 23,808.00 =
34,790.00
Calculate the Future Investment Value
at the end of the compounding period:
34,790.00 × (1 + 0.1)1 =
34,790.00 × 1.10 =
38,269.00
Start year 2.
Duration: 360 days = a full compounding period.
Add the periodic contributions to the balance:
38,269.00 + 12 × 1,984.00 =
38,269.00 + 23,808.00 =
62,077.00
Calculate the Future Investment Value
at the end of the compounding period:
62,077.00 × (1 + 0.1)1 =
62,077.00 × 1.10 =
68,284.70
Start year 3.
Duration: 360 days = a full compounding period.
Add the periodic contributions to the balance:
68,284.70 + 12 × 1,984.00 =
68,284.70 + 23,808.00 =
92,092.70
Calculate the Future Investment Value
at the end of the compounding period:
92,092.70 × (1 + 0.1)1 =
92,092.70 × 1.10 =
101,301.97
And the process goes along,
as detailed in the steps above.
The last two compounding periods:
Start year 5.
Duration: 360 days = a full compounding period.
Add the periodic contributions to the balance:
137,620.97 + 12 × 1,984.00 =
137,620.97 + 23,808.00 =
161,428.97
Calculate the Future Investment Value
at the end of the compounding period:
161,428.97 × (1 + 0.1)1 =
161,428.97 × 1.10 =
177,571.86
Start year 6.
Duration: 154 days = a partial compounding period.
Add the periodic contribution to the balance:
177,571.86 + 6 × 1,984.00 =
177,571.86 + 11,904.00 =
189,475.86
Calculate the Future Investment Value
at the end of the compounding period:
189,475.86 × (1 + 0.1)(154 ÷ 360) =
189,475.86 × (1 + 0.1)0.427777777778 =
189,475.86 × 1.041614149653 =
197,360.74