A more thorough explanation:

The actuarial method is a way to calculate the amount of interest on a loan. It uses the loan's annual percentage rate to figure out the finance charge for each payment period. After each payment is made, the amount is first credited to interest and then to principal.

For example, let's say you take out a loan with an annual percentage rate of 5%. Each month, you make a payment of $100. The actuarial method would calculate the interest on the loan for that month, which would be $4.17. The remaining $95.83 would then be applied to the principal balance of the loan.

The actuarial present value is the amount of money needed to purchase an annuity that would generate a specific monthly payment for the expected remaining life span of the recipient.

For example, let's say you want to purchase an annuity that will pay you $1,000 per month for the next 20 years. The actuarial present value would be the amount of money you need to invest now to ensure that you receive those payments for the next 20 years.

These examples illustrate how the actuarial method and actuarial present value are used in finance to calculate interest and plan for future payments.