Question

On March 20, Soren kierkegaard deposited $1000 into his savings account that pays 5.5% interest compounded daily. How much interest will the money earn by April 20?

Answer 1

Hey there! I'm happy to help!

There are 31 days in March, so there are 11 days left in March. We add this to the 20 days in April, giving us 31 total days this interest is compounded.

We could calculate the amount compounded each day for 31 total days, but that would take a long time. Instead, there is a formula we can use to calculate compound interest instead.

$Total= P(1+i)^n\\\\P=Principal Amount\\i=interest rate\\\\n=number of times compounded$

So, let's plug in those numbers! Remember to convert the percent to a decimal so it works in the equation!

$Total=1000(1+0.055)^3^1\\Total=1000(5.258068609)\\Total=5258.068609$

Now, we subtract the initial amount just to see how much interest was earned.

5258.068609-1000=4258.07 (rounded to nearest cent).

Therefore, the money will have earned $4,258.07 by April 20.

Have a wonderful day!