Calculate the Future Investment Value and the Compound Interest earned by a principal of 1,010.00 (Dollar, Euro, Pound, ...), initial amount of money lent, deposited or borrowed, with a duration of 3 years, 9 months and 29 days, 7.67% annual interest rate, compounded annually (once 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
[2] Future Investment Value, FV
Calculation formula:
FV =
P × (1 + r/n)n×t
FV, Future Investment Value
P, Principal (initial amount), P = 1,010.00
r, Annual compound interest rate, r = 7.67%
n, Number of times the interest compounds during a year
Compound frequency: annually (once a year)
n = 1
r/n = 7.67%/1 = (7.67 ÷ 100)/1 = 7.67/(100 × 1)
r/n = 0.0767
t, Duration of the investment
n×t, Duration of the investment, related to n
n×t =
+ 3 years
+ 9 months ÷ 12 months / year
+ 29 days ÷ 360 days / year
n×t ≈ 3.830555555556 years
Calculate FV
Substitute for the values in the FV formula:
FV =
P × (1 + r/n)n×t =
1,010.00 × (1 + 0.0767)3.830555555556 =
1,010.00 × 1.07673.830555555556 =
1,010.00 × 1.32721286081 ≈
1,340.48
[3] Compound interest amount, CI
Calculation formula
CI = FV - P
CI, compound interest amount
FV, Future Investment Value
P, Principal (initial amount)
CI ≈
1,340.48 - 1,010.00 ≈
330.48
[4] Project Breakdown. Annually.
Interest compounded: annually (once a year).
| Year | Days | Interest | Total
interest | Balance |
|---|
| 0 | 0 | -- | -- | 1,010.00 |
| 1 | 360 | 77.47 | 77.47 | 1,087.47 |
| 2 | 360 | 83.41 | 160.88 | 1,170.88 |
| 3 | 360 | 89.81 | 250.68 | 1,260.68 |
| 4 | 299 | 79.80 | 330.48 | 1,340.48 |
| Year | Days | Interest | Total
interest | Balance |
Answer:
Principal (initial amount) = 1,010.00
Future Investment Value = 1,340.48
Compound interest amount = 330.48
More calculations on Compound Interest and Future Investment Value:
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
Compound interest.
Interest. Simple and compound interest. Differences.
- When someone lends money to someone else, the borrower usually pays a fee to the lender. So the due interest is a sum paid or charged for the use of money or for borrowing it. The interest depends on:
- 1) the duration of the loan
- 2) the initial amount of money lent or borrowed, called principal
- 3) the interest rate (the percentage of the principal charged as interest)
- 4) the compound frequency.
- Number 4 in the list above, the frequency of the compounding interest, also makes the difference between compound and simple interest.
1. Simple Interest...
- ... is calculated only at the end of the loan period as a fixed percentage of the borrowed amount.
2. Compound Interest...
- ... is calculated not only at the end of the loan period, but periodically, over shorter periods of time, for example daily, weekly, monthly, ... These shorter periods are called compounding periods.
- The interest compounding frequency shows us how often is the interest calculated over the loan period. If the interest is calculated daily - then we have a daily compounding frequency, and the interest is said to be compounded daily. If it is calculated weekly - then we have a weekly compounding frequency, and the interest is said to be compounded weekly. And so on, monthly, quarterly, half-yearly, annually, ...
- The amount that results as an interest at the end of such a shorter compounding period is immediately added to the principal amount, so that the interest accrued up to that point contributes to the calculation of the interest for the next compounding period, and not only the principal amount, as it was in the case of simple interest.
- Thus, in the end, the interest also earns interest and not just the principal. It follows that the compound interest will produce a slightly higher amount in the form of interest than the simple interest.
How is the compound interest being calculated?
- If the annual interest rate is r% and the interest compounding frequency is annual, then it means that the compounding period is one year long and the interest is calculated once a year.
- 1. In one year, for the amount of P, an interest of (r% of P) is earned:
- C1 = r% × P
- The total amount accumulated after one year is:
- A1 = P + C1 = P + r% × P = P × (1 + r%)
- 2. After the second year, the interest is:
- C2 = r% × A1 = r% × P × (1 + r%)
- And the total amount is:
- A2 = A1 + C2 = P × (1 + r%) + r% × P × (1 + r%) = P × (1 + r%) × (1 + r%) = P × (1 + r%)2
- 3. After three years, the accrued interest is:
- C3 = r% × A2 = r% × P × (1 + r%)2
- And the total amount is:
- A3 = A2 + C3 = P × (1 + r%)2 + r% × P × (1 + r%)2 = P × (1 + r%) × (1 + r%)2 = P × (1 + r%)3
- n. After n years, the interest is:
- Cn = r% × An-1 = r% × P × (1 + r%)n-1
- And the total amount is:
- An = An-1 + Cn = P × (1 + r%)n-1 + r% × P × (1 + r%)n-1 = P × (1 + r%) × (1 + r%)n-1 = P × (1 + r%)n