Please show all work and equations

formulas given

Three years after 25 years of saving. Lucy withdrew $9,500 each year for a period of 4 years. In the fifth, sixth, and seventh years, she only withdrew $7,000 per year. In the eighth year, she decided to withdraw the remaining money in her account. If Lucy has saved $1,300 each year with an interest rate of 5% per year compounded monthly throughout the whole period, what was the amount she withdrew at the end of the eighth year? Draw a cash flow diagram for the given transactions and show all of your calculations. Nominal and effective interest rate EFFECT(nominal_rate, npery) F = P(1 + i)N FPIF/P, I, N) Fvfratenper,pmt.pv.type) i = NF/P-1 nominal rate m-time i-effective interest rate NOMINAL (effect_rate, npery) PPresent amount, F future amount, N time periods i interest rate Interest Rate log(F/P) log (1 + i) P = F(1 + i)-N PF(P/F, 1, N) Piratenper,pmt.fv.type) P-Af(1+0) - - A(F/A,1%,N) F= A(F/A,1%,n). A(P/A,1%,N) P AP/A,1,N). + N-11 v -F(A/F1%,N) A = F(A/F,1%,N). PMT(ratenper.pv.fv.type) i% ) AP(A/P,1%,N). PMTratenper.pv.fv.type) NPER(rate, pmt, pv, fv, type) [ --[+-] RATE(nper.pmt(A),Pv, Fv) Deferred Annuities P = A(P/A,1%, N-J)(P/F,1%, J) P = G(P/G, i%, N). A = G(A/G, 1%, N). present value of a geometric series Iff i ALMERN ANOPE.%.1) present value occurring at the end of period N I , (1 + ik) (P/F,r%, N) = e-rN (F/A, r%, N) = e'N 1 erN 1 (P/A, 1%, N) = erN (e 1)