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Is the 4.75% interest rate on my student loans compounded daily? Is it best to take out a home equity loan at 6% to pay them off more quickly / pay down half based on how the interest is calculated?

You owe some amount of student loans at a 4.75% interest rate. You are able to secure a home equity loan at a 6% interest rate. You want to know if the home equity loan would help you save money.
To answer your question I’m going to assume your 4.75% student loan interest rate is fixed (meaning it doesn’t increase or decrease with the market).
Interest on student loans does accrue daily. Some home equity loans also accrue interest daily but others accrue monthly. In order to worry about compounding interest on your student loan your payments would have to be less than the amount of interest that accrues between payments. Typically this means your monthly payment is less than the amount of interest that accrues each month.
Let’s look at your interest cost with both options. Interest is calculated according to the daily simple interest formula (loan balance X  interest rate)/ 365 .
Let’s say you owe $40,000 in student loan debt.
At your current rate of 4.75% you will accrue about $5.21 of interest daily or about $160 each month.
At an interest rate of 6% you will accrue about $6.58 of interest daily or about $200 each month.
It doesn’t add up financially to take out a higher interest loan to repay your student loans that have the lower interest rate. If you have federal student loans, paying them off with a home equity loan will shift your debt to a lender that likely doesn’t offer income-based repayment options, loan forgiveness, or other federal student loan benefits.
Let’s assume you aren’t making any payments and the student loan interest compounds on itself daily at a rate of 4.75% and the home equity loan compounds on itself monthly at a rate of 6%. Your balance after one year of the 4.75% interest rate would be $41,945. At a 6% interest rate your end of the year balance would be $42,467.
Any way you slice it the 6% interest rate is going to cost you more money. Stick with your 4.75% interest rate!