Calculate the daily compounding interest of a $1575 loan

How would you calculate this question to get the total interest earned?
Principal: $1575
Interest rate: 0.75%
Time invested: 85 days
Compounding frequency: Daily
STEP 1:    You are required to calculate the amount of interest obtained by daily compounding. The formula used for finding compound interest is:

compound interest formula

Here, P denotes the principal, r represents the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

STEP 2:    The rate of interest is 0.75% per year. Before beginning the calculations, you need to express 0.75% as an equivalent decimal number. This can be achieved by dividing 0.75 by 100.

converting 0.75 percent to decimal

STEP 3: The time invested is 85 days. It is a known fact that a year consists of 365 days. If we divide 85 days by 365 days, we get the equivalent number of years.

Converting days to years

STEP 4:    Since the interest is being compounded daily, you can take n as 365. Now that all the variable values are known, you can directly substitute them in the formula and get the result.

Using the compound interest formula

The interest earned after 85 days by daily compounding is about $1577.75 - $1575 = $2.75.

Comments for Calculate the daily compounding interest of a $1575 loan

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May 21, 2015
RE: Error in result
by: Visual Math

Thanks for telling us about the error, Dave! We're working on something new, so if you're interested, have a look here:

Jan 11, 2011
Error in result
by: Dave

I rated it 4 stars because ratings of 4.8 or 4.9 were not available. I couldn't give it 5 because of the error in the result putting the interest earned at a whopping $1577.75 with a minuscule interest of 0.75% after only a measly 85 days! This a 100.17% increase! whew! Obviously this is a silly error which math teachers are quite fond of penalizing more severely.
So take 4.9 stars for an otherwise exceptionally clear and concise explanatory example of a potentially complex topic in which other sites failed miserably.

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