Q3) Maria Garcia has an (arithmetic) annuity immediate that will make 10 annual payments. The first payment is P = $1000 and payment increases by Q = $100 from the payment before. The effective annual interest rate is i = 2.75%.

a) Compute both the present and future value of Maria Garcias annuity by showing it is equivalent to the following 2 annuities:

Annuity A: Level pay, $900 for 10 years Annuity B: Arithmetic increasing annuity immediate: starts today, lasts 10 years, first payment P = $100, increment Q = $100.

b) Write down formulas for the PV and FV of any similar arithmetic annuity immediate with first payment P, increment Q, n periods, and effective rate per period i.