Mahtab wrote:
There are two types of interest rates that GMAT handles with.
1) Simple interest
2) Compound Interest
simple interest is basically when you simply multiply your investment amount * interest rate * number of years.
Compound interest formula is \(Interest Earned = A * (1+i)^n - A\), where A is your investment amount.
The difference between the two can be conveyed with the following example:
Suppose you invest 5000 dollars in a bank with an interest rate of 10% for 3 years.
Compounded Annually:
After 1 year, your bank total would be: [$5000 * 0.10] + $5,000 = $5,500. (Total interest earned = $5,500 - $5000 = $500)
After 2 years, your bank total would be:[$5,500 * 0.10] + $5,000 = $6,050. (Total interest earned = $6,050 - $5000 = $1050)
After 3 years, your bank total would be: [$6,050 * 0.10] + $5,000 = $6655. (Total interest earned = $6,655 - $5000 = $1,655)
*Using the compounded interest formula above will give you the same answer.*
Whereas, simple interest for the same investment would be:
After 1 year, your bank total would be: $5,000 * 0.10 * (1) + $5,000 = $5,500. (Total interest earned = $5,500 - $5000 = $500)
After 2 years, your bank total would be: [$5,000 * 0.10 * 2] +$5,000 = $6,000. (Total interest earned = $6,000 - $5000 = $1000)
After 3 years, your bank total would be: [$5,000 * 0.10 * 3] + $5,000 = $6,500 (Total interest earned = $6,500 - $5000 = $1,500)
As you can see, "Compounded annually" charges interest on the bank balance which includes both the initial investment amount + the cumulative interest earned from that investment whereas simple interest is based solely on the interest earned from just the initial investment amount.
What does the term compounded annually mean ? interest received twice in a year? i.e once every 6 months ?