SOLUTION: #15: What lump sum deposited today at 12% compounded quarterly for 15 years will yield the same final amount as deposits of $5,000 at the end of each 6-month period for 15 years at

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Question 1088299: #15: What lump sum deposited today at 12% compounded quarterly for 15 years will yield the same final amount as deposits of $5,000 at the end of each 6-month period for 15 years at 6% compounded semiannually? Round to the nearest cent as needed.
Found 2 solutions by mathmate, MathTherapy:
Answer by mathmate(429)   (Show Source): You can put this solution on YOUR website!
Question:
What lump sum deposited today at 12% compounded quarterly for 15 years will yield the same final amount as deposits of $5,000 at the end of each 6-month period for 15 years at 6% compounded semiannually? Round to the nearest cent as needed.

Solution:
Step 1:
find the future value of $6000 deposited every 6 months for 15 years at APR=6%.
A=6000
n=2*15=30
i=0.06/2=0.03
F=A((1+i)^n-1)/i=6000(1.03^30-1)/0.03=285452.49
Step 2:
Find present value of future $285452.49 if deposited at 12% compounded quarterly for 15 years.
Convert future value to present value
F=285452.49
n=15*4=60
i=0.12/4=0.03
P=F(1+i)^n=285452.49/(1.03^60)=48450.73
Answer: A deposit (present value) of 48450.73 at 12% compounded quarterly for 15 years will yield the same accumulated (future) value as $6000 deppsited at every 6 months earning 6% interest compounded every six months for 15 years.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

#15: What lump sum deposited today at 12% compounded quarterly for 15 years will yield the same final amount as deposits of $5,000 at the end of each 6-month period for 15 years at 6% compounded semiannually? Round to the nearest cent as needed.
Correct answer: 

IGNORE all others who say otherwise! 

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