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### Course: Finance and capital markets>Unit 1

Lesson 2: Interest basics

# Compound interest

In this video, we expand the equation to calculate simple interest for a single period, P*(1+r), to calculate interest when interest is charged for more than one period and that interest is compounded at different intervals. By doing so, we can better understand the difference between simple and compound interest. Created by Sal Khan.

## Want to join the conversation?

• I have an equation for compound interest that states A = P(1+r)t. What does A stand for?
• A is total amount that you have during that year
• Wait... I was taught that for simple interest you have to do b=prt (balance= principal times interest rate x time). I did the first one with you (\$50 at 15% for 20 years) and I got \$150 dollars. Can someone help me with this?
• Sal is calculating what you'll pay in total, that's the principal plus the interest.

The equation you posted only calculates interest.

So when you take out a loan you have to pay the loan back, but you also pay interest accumulated on it. If you borrow \$50 at 15% simple interest for 20 years, you'll pay back \$50, plus 15% of \$50 20 times, or \$50 + (\$50 * 15% * 20), which you'll notice is p+prt

It's important to know whether you're calculating just the interest, or the total loan.
• Where did he get the one from: 50(1+(20 x .15))
• \$50 is the princ. To calculate the simple interest for 20 years at the rate of 15% , you will have
50 + 50(20*15/100) . So when you take the 50 out common, you will have
50( 1 +(20*.15) . There's where the 1 comes from.
• how do I figure out the interest paid on an investment?
• When you make an investment the total you get back (T) is the original ammount (O) plus an additional ammount (A) / Hence T=O+A.
The interest rate (I) is the ratio between the Additional ammount and the original ammount I=A/O so:T=O+O*I. Hence I=(T-O)/O;
eg if you intested 100\$ and received back 101\$ then the iterest is: I=(101-100)/100=0.01=1%
• How would you find and unkown rate? Like, for example, your balance is \$563, the principal is \$500, the rate is unkown and the time is 7 years? The answer is 1.8%, but I don't know how to get that.
• Solve for r, 500*(1+r)^7=563, or if you have excel use the RATE function =RATE(7,0,500,-563,0,0) which will give you 1.71%. The 7 is number of periods t=7 (nper), the payment(pmt) is what you contribute yearly, in our case 0 (you do not put any extra money towards the savings after each period), the present value (pv) of the money at t=0 is 500, the future value (fv) is the amount you want your money to grow at t=7, and that is 563(add a - here), the other 2 values are 0,0. Hope this helps a bit xD
• What is with the (+1) everytime he writes an equation?
• If you have \$1 and you earn interest of 5%, then you have \$1.05, not 0.05.
• Does the interest percentage have a 1:1 ratio? Like, he said the interest was 10%, so the money owed was \$10. Does that mean if the interest is 7%, the money owed is \$7?
• The percentage is based of whatever the loan was. If the loan was \$100 with 10% interest then, the money you owe is \$110 (\$10 increase). But, if the loan was \$50 with 10% interest then the, money you owe is \$55 (\$5 increase)
• why is the quality kinda bad
• It's probably an older video. Sal started on YT a long time ago.
(1 vote)
• If I earned \$400.00 at 4% interest, what was my original investment?