Please enable JavaScript.
Coggle requires JavaScript to display documents.
COMPOUND INTEREST ((A few people have written to me asking me to explain…
COMPOUND INTEREST
A few people have written to me asking me to explain step-by-step how we get the 8235.05. This all revolves around BODMAS / PEMDAS and the order of operations. :
Using the order of operations we work out the totals in the brackets first. Within the first set of brackets, you need to do the division first and then the addition (division and multiplication should be carried out before addition and subtraction). We can also work out the 12(10). This gives us...
-
(note that the over-line in the calculation signifies a decimal that repeats to infinity. So, 0.00416666666...)
-
-
The exponent goes next. So, we calculate (1.00416) ^ 120.
-
-
-
-
An investment earns 3% compounded monthly. Find the value of an initial investment of $5,000 after 6 years.
-
-
Earns 3% compounded monthly: the rate is r=0.03 and the number of times compounded each year is m=12
Initial investment of $5,000: the initial amount is the principal, P=5000
-
You are trying to find A, the future value (the value after 6 years). Now apply the formula with the known values:
-
Answer: The value after 6 years will be $5,984.74.
-
If an amount of $5,000 is deposited into a savings account at an annual interest rate of 5%, compounded monthly, the value of the investment after 10 years can be calculated as follows...
-
-
-
-
If we plug those figures into the formula, we get the following:
-
So, the investment balance after 10 years is $8,235.05.
-
To use the compound interest formula you will need figures for principal amount, annual interest rate, time factor and the number of compound periods. Once you have those, you can go through the process of calculating compound interest.
The formula for compound interest, including principal sum, is:
-
-
What is the value of an investment of $3,500 after 2 years if it earns 1.5% compounded quarterly?
-
As before, we are finding the future value, A. In this example, we are given:
-
-
-
-
-
Answer: The value after 2 years will be $3,606.39.
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics.
Compound interest is calculated by taking your figures for the principal amount, interest rate, time period and compound frequency and entering them into the compound interest formula to return the amount of interest you might accrue over that time period.
-
The benefit of compound interest
I think it's worth taking a moment to examine the benefit of compound interest using our example. The benefit hopefully becomes clear when I tell you that without compound interest, your investment balance in the above example would be only $7,500 ($250 per year for 10 years, plus the original $5000) by the end of the term. So, thanks to the wonder of compound interest, you stand to gain an additional $735.05.
-
Interactive compound interest formula
I have created the calculator below to show you the formula and resulting accrued investment/loan value (A) for the figures that you enter. Note that this calculator requires