# How is interest calculated on a UK type 1 student loan?

On my student loan annual statement it says The Student Loan Company applied interest to my balance every month but only received one lump sum payment at the end of the year from HMRC, even though they collect my student loan repayments monthly through payroll.

Does this mean I'm losing out because of compound interest due to HMRC hoarding my money?

You're unlikely to be losing out
Unless the amount you repaid each month went down throughout the year, you wont lose out due to compound interest. This is because when the SLC receives the annual lump sum of payments that HMRC collected from you, they assume 12 equal monthly payments were made and retrospectively calculate the interest accordingly.

How to verify this yourself
For any given month on your statement:

1. Take the AER for the given month which you can find here.

Currently that is 1.75% (Bank of England base rate + 1%)

1. Find the equivalent daily rate by calculating the 365th root of your AER

1.0175 ^ (1/365) = 1.0000475316455781361 (Approx 0.0048%)

1. Find the equivalent rate for the specific month you're looking at by taking this daily interest rate and raise it to the power of the number of days in the month you're interested in.

For August that gives 1.0000475316455781361 ^ 31 = 1.00147453205044079 (Approx 0.147%)

1. Use this to calculate the interest for that month, assume starting balance of £20,000

£20,000 * 0.00147453205044079 = £29.49

1. To calculate the new balance, take the opening balance, add the interest and subtract 1/12th of your annual payment. So if you paid £1200 over the year that gives:

£20,000 + £29.49 - £(1200/12) = £19,929.49

Repeat these calculations for each month and you should be able to match the SLC calculations for the closing balance to withing a few pence.

If you're using excel to do this, you can use `=POWER(1.0175,1/365)` to calculate the daily interest rate. If that formula is in cell A1 you can then use `=POWER(A1,30)` to calculate the monthly interest rate.

Note: This is a self answer after I got cheesed off thinking I was losing out and sat and verified this for myself. Posting because I've seen people on other forums who have had the same thoughts.