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 formula to be used is S =R R = S Smi S120.10 R = 10000. S210.10 |(1.10)/12 –1 R = 10000 0.10 (1.102 – 1 0.10 |(1.10)/12 –1 (1.10)2 -1 R = 10000 R = 379.72 I 10000 x ( 1.10 ^ ( 1 +12) - 1 ) +(1.10^2 - 1) = 379.72
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 formula to be used is S =R R = S Smi S120.10 R = 10000. S210.10 |(1.10)/12 –1 R = 10000 0.10 (1.102 – 1 0.10 |(1.10)/12 –1 (1.10)2 -1 R = 10000 R = 379.72 I 10000 x ( 1.10 ^ ( 1 +12) - 1 ) +(1.10^2 - 1) = 379.72
Chapter9: Sequences, Probability And Counting Theory
Section9.4: Series And Their Notations
Problem 56SE: To get the best loan rates available, the Riches want to save enough money to place 20% down on a...
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Transcribed Image 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
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