Sample Practice Problem
ID: #GAOAD
A participant in the municipal archive preservation program wants monthly income of \(2,800\), beginning immediately at retirement. At retirement, each \(1,000\) paid to the provider purchases \(9.20\) of monthly lifetime income. Beginning today, the participant makes \(288\) equal monthly deposits into a fund earning a nominal annual rate of \(8\%\), compounded monthly. The final deposit is made one month before retirement. Calculate the required monthly deposit.
(A)348.8535
(B)232.5690
(C)346.1465
(D)29.5270
(E)261.6401
📖 Worked Solution & Strategy
The retirement purchase price is \(2,800(1,000)/9.20=304347.83\). Because deposits begin today, they form an annuity-due. With monthly rate \(j=0.080/12\), their retirement value is \(X\ddot{s}_{288|j}\). Hence \[X=\frac{304347.83}{\ddot{s}_{288|0.080/12}}=348.8535.\] Thus each monthly deposit must be \(348.85\).
Therefore, the result is \(\frac{207177505346766016038106721627916204840716724957478026019338598499831921745230994668412200994276650507621082780428743195290411085612881892046626658464428577094971491489140661267928488294381208688047368549695661853494120969377093398869218753361904050608196821452934742543444755599100366307201370958193664684188206592807546257972717285156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{64552290819445489150164502025441630612900724627702216949200151465493562752801651074487349642985982017405523505388276151216365941927003054224937580187671755532386463309415486728170095498353360497463690616399206990309595642358023319659675939777302091017778533937201431258586994023234786495151012565457159652804419700677029761956994787234152449738311846101755113984841663012659469116611948978664719880613516083839757155603694093701450132937981420052384788593878827716543725935766892088611740428361295842807813629999705032409295644332124536770727152802466165029311132554035367171685752640663828218563830674385819065268551356507486193 a}\approx 348.8535\), so the correct answer is option (A).
Final Answer: Option (A)
Unlock Full Step-by-Step Solution & Practice
Get instant access to this worked derivation plus procedurally generated practice questions for Exam FM.