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Question 1143251: Bobby would like to take a trip to Greece in 5 years. He will need $1,575 monthly while he is there and expects to remain there for 8 months. If money is worth 3.9% compounded monthly, how much will Bobby need to deposit now in order to make his trip to Greece become a reality? Assume he will need the money at the BEGINNING of each month.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! he will need 1575 at the beginning of each month for 8 months.
the money is worth 3.9% compounded monthly.
there are two pieces to this problem.
first is to find the present value of the annuity for 8 months.
second is to find the present value of that amount for 5 years.
both these amounts can be found by formula or by calculator.
i'll do calculator.
if you need formula, then come back to me and i will give you bormula.
the clculator i used is the TI-BA-II business analyst calculator.
my inputs to this calculator for the annuity are:
present value = 0
future value = 0
payment at the beginning of each is 1575 for 8 months.
interest rate percent per month is 3.9/12 = .325.
calculator tells me that the present value for the annuity is equal to 12,458.06115
that's the amount of money needed in 5 years.
that's the future value of an amount of money for 5 years at 3.9% per year compounded monthly.
i then tell the calculator the following.
present value = 0
future value = 12,458.06115
monthly payment = 0
interest rate percent per month = 3.9 / 12 = .325.
time period is 5 years * 12 = 60 months.
calculator tells me that the present value is equal to 10,254.16624.
i repeated the procedure with an online financial calculator that tells me the following.
i basically used the same procedure as i did with the TI-BA-II calculator.
this calculator can be found online at https://arachnoid.com/finance/
the calculators require that, if the payment is negative, than the present value or future value will be positive.
they also require that, if the present value is negative, the future value will be positive, and vice versa.
where you have to remember this is when you input both present value and payment, or present value and future value.
one of them has to be negative and the other has to be positive or the calculator will not be able to give you a result.
the cash flow rule is that money going out is negative and money coming in is positive.
for example, you wanted 1575 to come in to you each month, so that is positive.
the investment required to get that (the present value) is therefore shown as negative because that's money you have to shell out at the beginning of the 8 month period.
the difference between what the TI-BA-II calculates and what the online calculator calculates is due to rounding.
the TI doesn't round intermediate results.
the online calculator does (rounds to the nearest penny as far as i can tell).
the difference is usually minimal, as can be seen in the results shown for both.
any questions, contact dtheophilis@gmail.com
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