Calculate the Future Investment Value and the Compound Interest earned by a principal of 1,000.00 (Dollar, Euro, Pound, ...), initial amount of money lent, deposited or borrowed, with a duration of 2 years, 4.00% annual interest rate, compounded half-yearly (twice a year)

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


Note: half a year = 1 semester


Number of days in a semester = 180


Number of semesters in a year = 2


[2] Future Investment Value, FV
Calculation formula:

FV =


P × (1 + r/n)n×t


FV, Future Investment Value


P, Principal (initial amount), P = 1,000.00


r, Annual compound interest rate, r = 4.00%


n, Number of times the interest compounds during a year
Compound frequency: half-yearly (twice a year)
n = 2


r/n = 4.00%/2 = (4.00 ÷ 100)/2 = 4.00/(100 × 2)
r/n = 0.02


t, Duration of the investment
n×t, Duration of the investment, related to n

n×t =

+ 2 years × 2 semesters / year

n×t = 4 semesters


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


Calculate FV
Substitute for the values in the FV formula:

FV =


P × (1 + r/n)n×t =


1,000.00 × (1 + 0.02)4 =


1,000.00 × 1.024 =


1,000.00 × 1.08243216 ≈


1,082.43


[3] Compound interest amount, CI
Calculation formula

CI = FV - P


CI, compound interest amount

FV, Future Investment Value

P, Principal (initial amount)


CI ≈


1,082.43 - 1,000.00 ≈


82.43


[4] Project Breakdown. Half-yearly.

Interest compounded: half-yearly (twice a year).

Semester Days Interest Total
interest
Balance
0 0 -- -- 1,000.00
1 180 20.00 20.00 1,020.00
2 180 20.40 40.40 1,040.40
3 180 20.81 61.21 1,061.21
4 180 21.22 82.43 1,082.43
Semester Days Interest Total
interest
Balance

Answer:

Principal (initial amount) = 1,000.00

Future Investment Value = 1,082.43

Compound interest amount = 82.43


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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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