An amount, P, must be invested now to allow withdrawals of $1,200 per year for t

Question

An amount, P, must be invested now to allow withdrawals of $1,200 per year for the next 13 years and to permit $320 to b withdrawn starting at the end of year 5 and continuing over the remainder of the 13-year period as the $320 increases by 5% per year thereafter That is, the withdrawal at EOY six will be $336.00, $352.80 at EOY seven, and so forth for the remaining years. The interest rate is 12% per year Click the icon to view the interest and annuity table for discrete compounding when i= 5% per year. Click the icon to view the interest and annuity table for discrete compounding when 12% per year The P amount is (Round to the nearest dollar)

Explanation / Answer

Sum=-P+1200/1.12+1200/1.12^2.........1200/1.12^13+320/1.12^5+320*1.05/1.12^6...........

This should eqaul zero,

0=-P+1071.42857142857+956.632653061224+854.136297376093+762.621694085797+680.912226862319+607.957345412785+542.819058404272+484.659873575243+432.732029977895+386.367883908835+344.971324918603+308.010111534467+275.009028155774 +181.576593829952+170.22805671558+159.588803170856+149.614502972678+140.263596536885+131.49712175333+123.278551643747+115.573642166013+108.350289530637

So,P=8988.229

Alternatively,

-P+1200/1.12*(1-(1/1.12^13))/(1-1/1.12)+320/1.12^5*(1-(1.05/1.12)^9)/(1-(1.05/1.12))=0

So, P=8988.229

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