00:01
So if $7 ,000 is our initial amount and we're going to invest it in a bank at an interest of 5 % annual, then we want to find the amount in, the term is 9 years, first when we compound annually, so 1 annual.
00:31
Then our formula for the amount at time t is the initial amount 7 ,000, so at amount at time t is a0 times 1 plus r to the t, where r is the interest per compounding period t.
01:04
So here we have compounding period of 1 year, so r is 5 % or 0 .05 and our t is 9 because each compounding period is 1 year, so we get the amount after 9 years is equal to 7 ,000 times 1 .05 to the 9, which is equal to 10859 .3, so $10 ,859.
01:40
And two, we want to use quarterly compounding, so quarterly, so that means that per quarter, per compounding period, our r is equal to 0 .05 divided by 4, which is 0 .0125, and our term is 9 years times 4 quarters is 36 quarters, so our amount after 9 years will be 7 ,000 times 1 .0125 to the t, which is 36 quarters, and that gives us $10 ,947 .61, so that clearly is more than if we compound monthly...