Question 1088298: #12: Find the payment that should be used for the annuity due whose future value is given. Assume the compounding period is the same as the payment period. $12,000; quarterly payments for 14 years; interest rate 7.2%
Found 2 solutions by mathmate, MathTherapy:
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website! Question:
Find the payment that should be used for the annuity due whose future value is given. Assume the compounding period is the same as the payment period. $12,000; quarterly payments for 14 years; interest rate 7.2%
Solution:
The future value of quarterly payments of $12000 for 14 years at 7.2%
F=120000((1+0.072/4)^(4*14)-1)/(0.072/4)
=1143774.05
Initial deposit to contract the quarterly payments
P=F/(1+.072/4)^(4*14)
=1143774.05/(1.018^(56))
=194136.30
$194136.30 is required to purchase the annuity that pays $120000 quarterly for the next 14 years.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
#12: Find the payment that should be used for the annuity due whose future value is given. Assume the compounding period is the same as the payment period. $12,000; quarterly payments for 14 years; interest rate 7.2%
An ANNUITY DUE denotes payments being made at the BEGINNING of the period, as opposed to the end of the period.
Hence, payment to be made every BEGINNING-OF-QUARTER, for 14 years, at a QUARTERLY compounding rate of 7.2%: 
If payments were to be made every END-OF-QUARTER, for 14 years, at a QUARTERLY compounding rate of 7.2%, then each payment would be: $125.90.
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