# algebra

Find the amount of periodic payment necessary for the deposit to a sinking fund. (Round your answer to the nearest cent.)
Amount Needed A \$50,000
Frequency n semiannually
Rate r 11%
Time t 15 years

Thank you for your time, it is appreciated.

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1. Future value = 50000
period = semi-annual
number of periods, n = 15*2=30
Annual interest rate, = 11%
i = 0.11/2=0.055
Periodic payment (6 months) = P

Let r=1+i=1.055

Future value, 50000
= P(1+r+r²+r³+...+rn-1)
= P(rn-1)/(r-1) by factorizing

therefore, using (r-1)=i,

P=50000*i/(rn-1)
=50000*0.055/(1.05530-1)
=690.27 per period of 6 months.

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