i had a test today and i was confused on the intrest part, i mean i should have known what i was doing, but i felt that i bombed the questions because i did the wrong intrest, so can you please tell me the difference
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Sure can, Trevor.
Simple interest is simple proportion. If interest is 10% per year simple interest, then after 2 years it's twice as much (20%), after 3 years three times as much (30%), and so on.
Compound interest starts off the same. If interest is compounded at the end of the year, it's 10%, the same as simple interest. But what happens next is that the interest is added to the amount invested or borrowed, so we start the second year with 110% of the amount instead of 100%.
At the end of the second year, when simple interest would have been another 10%, making 20% over the two years, compound interest would add 10% of 110%, making 21% after 2 years.
This interest would then be added again to the amount, so that at the beginning of the third year we have 121% of the original amount, and 10% of this comes to 12.1% at the end of the year. The simple interest would be 30% but the compound interest would be 33.1%.
Over a long period of time compound interest well outstrips simple interest, and that's why mortgages are usually so expensive because compound interest applies for 25 years typically.
If r is the interest rate %, then simple interest after T years on an initial amount P is PTr/100.
Compound interest is (P(1+(r/100))^T)-P. Simple interest is to compound interest what an arithmetic progression is to a geometric progression, roughly speaking.
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