[Allen Farber]

Can someone please tell me how compound interest works with this example (not a real scenario): I borrowed $70,000.00 from the bank at an APR of 5% for a period of 10 years. So doing the math, my monthly payments will be $742.46. So from there, explain to me how compound interest would work.

[ebaines]

Compound interest has to do with the earnings you make in a savings account or other investment where the bank pays you interest for keeping your money with them. The idea that as interest is added to your account each month the amount of money in the account grows, and therefore the amount of interest you earn each month grows. For example if you put $100 into a savings account earning 6% per year (which is equivalent to 0.5% per month), and if the bank credits interest to the account each month, then your account grows as follows:

Starting balance = $100.00
End of Month 1: interest earned is 0.005 x $100 = $0.50, new balance = $100.50
End of month 2: interest earned is 0.005 x $100.50 = $0.5025, new balance = $101.0025.
End of month 3: interest earned is 0.005 x $101.0025= $0.505013, new balance = $101.5075
End of month 4: interest earned is 0.005 x $101.5075= $0.507538, new balance = $102.0151
Etc.

Notice that each month the amount of interest gets bigger, because the amount of money earning the interest is getting bigger. Your interest is earning interest - that's what's meant by "compounding." In this case after 4 months you have $0.0151 more in your account than you would have if you were being paid simple interest at a flat rate 0.005% per month on the starting balance only (i.e. $0.50/month). The difference doesn't look like very much for this example, but over time it can be quite significant. For example the length it time it takes to double your investment when earning 6%/year is 16.67 years if earning simple interest, but with compound interest it takes only about 12 years.

Now, with respect to loans the equivalent idea is that as you pay off the loan over time the amount of interest you have to pay becomes less and less.

[Allen Farber]

Compound interest has to do with the earnings you make in a savings account or other investment where the bank pays you interest for keeping your money with them. The idea that as interest is added to your account each month the amount of money in the account grows, and therefore the amount of interest you earn each month grows. For example if you put $100 into a savings account earning 6% per year (which is equivalent to 0.5% per month), and if the bank credits interest to the account each month, then your account grows as follows:

Starting balance = $100.00
End of Month 1: interest earned is 0.005 x $100 = $0.50, new balance = $100.50
End of month 2: interest earned is 0.005 x $100.50 = $0.5025, new balance = $101.0025.
End of month 3: interest earned is 0.005 x $101.0025= $0.505013, new balance = $101.5075
End of month 4: interest earned is 0.005 x $101.5075= $0.507538, new balance = $102.0151
Etc.

Notice that each month the amount of interest gets bigger, because the amount of money earning the interest is getting bigger. Your interest is earning interest - that's what's meant by "compounding." In this case after 4 months you have $0.0151 more in your account than you would have if you were being paid simple interest at a flat rate 0.005% per month on the starting balance only (i.e. $0.50/month). The difference doesn't look like very much for this example, but over time it can be quite significant. For example the length it time it takes to double your investment when earning 6%/year is 16.67 years if earning simple interest, but with compound interest it takes only about 12 years.

Now, with respect to loans the equivalent idea is that as you pay off the loan over time the amount of interest you have to pay becomes less and less.

I am aware how it works if you're investing/saving, it's just I don't know how it can be applied to loan payments or be amortized.

[ma0641]

It is not compound interest on the loan. It is amortized over 10 years. Look up "Amortization tables", plug in 70,000 for 10 years, 5. %, 12 payments per year. What do you get?