A security deposit is a sum of money that a tenant provides to a landlord before moving into an apartment. The landlord typically refunds the security deposit when the tenant moves out, provided that the apartment's condition warrants a refund. The security deposit may begin to accrue interest under certain conditions specified in the lease. The calculation of the interest on a security deposit depends on the amount of the deposit, the interest rate and the compounding period on the interest.

Obtain the amount of the security deposit from the lease. For example, assume the security deposit is £65.

Retrieve the annual percentage rate, or APR, of the security deposit from the lease. Assume the APR on the security deposit is 5 per cent.

Divide the APR of the security deposit by 100 to obtain the annual interest rate of the security deposit. In the example, 5 per cent divided by 100 equals 0.05.

Record the compounding period for the interest on the security deposit from the lease. Assume the interest is compounded monthly, or 12 times per year.

Divide the annual interest rate of the security deposit by the number of times the interest is compounded in a year to obtain the interest rate for the compounding period. In the example, 0.05 divided by 12 equals 0.00417.

Obtain the number of compounding periods over which the interest on the security deposit has been accruing. Assume that the security deposit has been accruing interest for 14 months.

Calculate the current balance on the security deposit with the formula T = A * (1 + I)^N, in which T is the current balance on the security deposit, A is the initial security deposit, I is the interest rate for the compounding period and N is the number of compounding periods over which the interest on the security deposit has been accruing. In the example and using the formula, the current balance on the security deposit is 100 * (1 + 0.00417)^14 = £68.8.

Subtract the original amount of the security deposit from the current balance of the security deposit to obtain the interest on the security deposit. In the example, £68.8 - £65 = £3.80.