Question 1172747: Paul and Donna Kelsch are planning a Mediterranean cruise in 3 years and will need $9,500 for the trip. They decide to set up a "sinking fund" savings account for the vacation. They intend to make regular payments at the end of each 3 month period into the account that pays 6% interest compounded quarterly. What periodic sinking fund payment (in $) will allow them to achieve their vacation goal? (Round your answer to the nearest cent.)
Answer by ikleyn(52781)   (Show Source):
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Paul and Donna Kelsch are planning a Mediterranean cruise in 3 years and will need $9,500 for the trip.
They decide to set up a "sinking fund" savings account for the vacation. They intend to make regular payments
at the end of each 3 month period into the account that pays 6% interest compounded quarterly.
What periodic sinking fund payment (in $) will allow them to achieve their vacation goal? (Round your answer to the nearest cent.)
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It is a classic Ordinary Annuity saving plan. The general formula is
FV =  ,
where FV is the future value of the account; P is the quarterly payment (deposit);
r is the factual quarterly rate presented as a decimal;
n is the number of deposits (= the number of years multiplied by 4, in this case).
From this formula, you get for the monthly payment
P =  . (1)
Under the given conditions, FV = $9,500; r = 0.06/4; n = 3*4. So, according to the formula (1),
you get for the quarterly payment
P =  = $728.46.
Answer. The necessary quarterly deposit value is $728.46.
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On Ordinary Annuity saving plans, see the lessons
- Ordinary Annuity saving plans and geometric progressions
- Solved problems on Ordinary Annuity saving plans
in this site.
The lessons contain EVERYTHING you need to know about this subject, in clear and compact form.
When you learn from these lessons, you will be able to do similar calculations in semi-automatic mode.
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