7.5 UNKNOWN PERIODIC PAYMENTS Often, in a given problem, the present or future value, the interest rate and the number of periods are known and the size of the annuity is unknown. To determine the...

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Extracted text: 7.5 UNKNOWN PERIODIC PAYMENTS Often, in a given problem, the present or future value, the interest rate and the number of periods are known and the size of the annuity is unknown. To determine the size of an annuity is to find the periodic payment. Example 9. What monthly payment is needed to accumulate 10,000 due after 2 years at 10%? Solution: Given: (general ordinary annuity) S = 10,000, t = 2 years, i = 10%, p = 1, c = 12, k = 1/12 Since the annuity is a general ordinary annuity and the given is the accumulated value then the Sni S =R formula to be used is R = S Smi $1,20.10 R = 10000 Sz10.10 |(1.10)/12 -1 0.10 R = 10000 (1.10)? – 1 0.10 (1.10)/12 –1 (1.10)² – 1 R = 10000 R = 379.72 10000 x ( 1.10 ^ (1+12) - 1 ) +( 1.10 ^ 2 - 1) = 379.72