B21 Annuities Payable m-thly

Question 1

what is an “m-thly annuity”?

Answer 1

an annuity with m payments per year

Question 2

How do we find the present value of payments of 1/m every m-th of a year (total of 1 per year) for n years (a^(m) angle n) using the effective rate per payment period?

Answer 2

Treat it as m x n payments of 1/m every m-th of a year, and use a regular annuity:

a^(m) angle n at a rate of i = 1/m * a angle m x n at a rate of i^m/m

Note: the coefficient of a^(m) angle n is the total annual payment

Question 3

How d we find the present value of payments of 1/m every m-th of a year (total of 1 per year) for n years (a^(m) angle n) using the fusion method?

Answer 3

Accumulate each year’s m payments to the end of the year, giving an n-year annuity with payments of 1/m * s angle m at a rate of i(m)/m:

a^(m) angle n at a rate of i = 1/m * s angle m at a rate of i^(m)/m * a angle n at a rate of i