Find the amount accumulated FV in the sinking fund. HINT [See Example 1.] (Assum

Question

Find the amount accumulated FV in the sinking fund. HINT [See Example 1.] (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest cent.)

$550 is deposited monthly for 19 years at 3% per year

FV= $____________

Find the present value PV of the annuity necessary to fund the withdrawal given. HINT [See Example 3.] (Assume end-of-period withdrawals and compounding at the same intervals as withdrawals. Round your answer to the nearest cent.)

$900 per month for 10 years, if the annuity earns 6% per year

PV=$________

Explanation / Answer

(1) monthly rate = 0.03/12
number of installments = 19*12

FV = PMT((1+r)^n-1)/r, with r & n adjusted for periodicity

= 550((1+.03/12)^(12*19) -1)/(.03/12)

(3) adjusting r & n for periodicity , the formula is
PV = PMT(1-(1+r)^-n)) /r

Here PMT=$900,    r=0.06/12,    n=12*10    
PV = 900(1-(1+0.06/12)^(-12*10))/(0.06/12) = $81,066.10

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