How to Calculate Annual vs. Continuous Compounding
When comparing two loans with the same interest rate, the loan with the greatest number of compounding periods per year will always have the higher effective interest rate. In other words, that will be the loan that is most expensive for you to take. Annually compounding loans will only compound once per year. Loans that continuously compound, however, will constantly be accumulating interest. There is a formula for calculating the effects of compound interest. Once you know the effects of annual compounding compared with continuous compounding, it is easy to compare the two.
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Instructions
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Find the result of an annually compounding loan using the following formula:
PV (1 + i)^n
Where PV is the amount of the loan, i is the interest rate and n is the number of years. Consider a $1,000 loan with an interest rate of 12 percent that has a length of one year. Your equation to solve this example would be:
1,000 (1 + .12)^1
The balance after one year would be $1,120.
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2
Find the result of a continuously compounding loan using the following formula:
PVe^i*y.
PV again represents the amount of the loan, e is the natural logarithm, whose approximate value is 2.71828, i is the interest rate, and y is the number of years. Using the same loan example as above, your equation for this loan would be:
1,000*2.71828^.12*1
Solving this equation results in the amount $1,127.50.
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3
Compare the two loans. The loan with annual compounding will have a balance of $1,120 after one year, and the loan with continuous compounding will have a balance of $1,127.50. Obviously, from a bank's perspective the loan with continuous compounding will be beneficial to them, as they will make more money. All other things being equal, more compounding periods equals more interest paid.
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