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Use Simple and Compound Interest
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Interest
There are two ways of calculating interest. It is either simple interest or compound interest.
Simple Interest
Simple interest is interest that is earned on an amount over a long period and calculated at the end of the period only.
Example: Joseph puts R 1 000-00 into a fixed deposit account at the bank. The interest he earns will be a fixed interest of 12% per year (p.a. is the official abbreviation for per year and it comes from the Latin words per annum).
After 12 months (one year) Joseph can expect his investment to have grown as follows:
R1,000-00 @ 12% interest p.a.= R1,120.00
The following formula for simple interest can be compiled: Where
P = Principal Amount
n = time in years
I = rate in percentage per annum
Simple interest - A = P(1+i.n)
From Joseph’s example we can see that:
The principal amount (P) is R 1 000-00
The time in years (n) is I
The rate in percentage per annum (i) is 12
To apply the formula, we simply substitute the figures in the correct places:
Simple Interest = P(1+i.n)
= 1 000 (1 + 12 (1))
= 120
The Increased value of an investment is called the amount and is calculated by adding the interest to the amount that was invested (Principal)
Amount = Principal + Interest
In Joseph’s case, the formula s applied as follows:
Amount = Principal + Interest
= 1 000-00 + 120
= 1 120
If Joseph invested the R1 000.00 for a period of 5 years, with the interest of 12% only payable at the end of the five years, his investment would have grown as follows:
The principal amount (P) is R 1 000.00
The time in years (n) is 5
The rate in percentage per annum (i) is 12
To apply the formula, we simply substitute the figures in the correct places.
Simple Interest = P (1 + (i) (n))
= 1000 (1 + 12(5)/100)
= 1000 x 0.12 x 5
= 1000 x 0,6
= 600
Amount = Principal + Interest
= 1000-00 + 600
= 1600
Compound Interest
Compound interest is interest that is earned on an amount over a longer or shorter period and calculated daily, weekly or monthly. This interest is then paid into the account and used to calculate the following day, week or month’s interest. In short, compound interest is interest earned on an amount plus its interest.
Compounding Rands
I gave my daughter a Ziploc bag with a handful of rand and told her over the course of a week I wanted her to give me one rand a day. For the next seven days, I would be her personal banker. I would deposit the rand in “The bank of Dad” and compound interest would begin to accrue the day she had deposited the rand. At the end of the week, we would check her balance at the “ATM” (Automated Tell –me-how-much-money-my dad-has for me Machine).
Each day my daughter handed over a rand at the breakfast table and I deposited one in her bank- which is really an old can fruit bottle. I gave her a “receipt” for her deposit and explain that she needs to keep up with the receipts to see how much money she has added to her account. In an effort to make this a little more realistic, I deposited a rand from my own piggy bank every other day to give her an additional four Rand at the end of the week. I could have just matched her rand for rand but didn’t want to set the unreal expectation that it is easy to double your money in a short time.
Balance Enquiry
On Sunday evening we gathered receipts and confirmed she had deposited seven rands in “ The Dad Bank” I asked her how much money that represented, and she correctly told me,” Seven Rand”. Using That ATM, she is familiar with, she performed a balance enquiry. I opened the can fruit container and counted out its contents- all eleven pennies. “Hey, there are four rands extra in here!”
Yes! She got it! I explained that her original seven rands had grown to eleven rands because every couple of days the bank paid her a rand for letting them use her money that's interest. I gave her back all the money and told her to put it into a savings envelope and to go and save it in the bank.
The Compound interest formula is:
A = P(1 + r/100)n
Where:
A is the amount or total value of the investment after a certain period
P is the principal that is invested at the beginning of the period
i is the rate in percentage per annum*
n is the number of periods, not necessarily years*
Should precious want to invest this R 1 000-00 over a five-year period, her investment will grow to the following amount:
A = Total value of the investment after 5 years
P = The principal amount of R 1 000-00
r = The rate for 5 years i.e. 12% per annum
n = Number of periods in 5 years i.e. 5(years) x 12 (months)
= 60 periods
A = P(1+ ʳ/100)ⁿ
= 1 000(1 + 1,12)
= 1 000(1,12)
= 1 000 x 1,1268247
= 1 126,8247
= 1 126,83
Interest = A - P
= 1 126,83 - 1 000
= 126,83
Example 1:
Richard invests R500 for 3 years at a rate of 8% per annum. Interest is compounded annually.
Value of the investment at the end of the 1st year: 8/100 x R500 =R35
At the end of year, 1st = R 500 + R35 =R 535
Value of the investment at the end of the 2nd year: 8/100 x R535 =R42.80
At the end of year 2 = R 535 + R42.80 =R 577.80
Value of the investment at the end of the 3rd year: 8/100 x R 577.80 = 46.22
At the end of year 3 = R 577.80 + R46.22 =R 624.02
Total compound interest after 3 years = R 624.02 – R 500 = R 124.02
Compare this to simple interest rates: R 500X 8/100X 3years =R 120.00
Example 2:
R1000 is invested at 8% p.a. compounded annually. Calculate the value of the investment at the end of six years.
Solution: Compounded annually means that the interest is added to the capital at the end of each year.
Value of the investment at the first year: R 1000x8/100 = R80
At the end of year 1= R1000 + R80 =R1080
Value of the investment at the 2nd year: R 1080x8/100 = R86.40
At the end of year 2= R1080 + R86.40 =R1166.40
Value of the investment at the 3rd year: R 1166.40x 8/100 R93.31
At the end of year 3= R1166.40 + R93.31 =R1259.71
End of the 4th year: 1259, 71 +0.08 (1259.71) = R 1 360.49
End of the 5th year: 1360.49 +0.08 (1360.49) = R 1 469.33
End of the 6th year: 1469.33 +0.08 (1469.33) = R 1 586.87
Interest over six years = R 1 586.87 -R 1000 = R586.87
Compare to simple interest over the same period.
A = P(1 +i.n)
= 1000 (1+0,08x 6)
= R1 480
So compound interest is a better option over long periods of time.
You will notice after 6 years of compound interest, the amount saved is R1 586.87, compared to only R1 480 using simple interest.
Click here to view a video that explains simple compound interest.