SOLUTION: Larger wants to take a trip in 8 years. She needs 2,400$. How much should she deposit into an account that pay 3.5% interest daily to meet her goal, round to nearest dollar

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Question 1208633: Larger wants to take a trip in 8 years. She needs 2,400$. How much should she deposit into an account that pay 3.5% interest daily to meet her goal, round to nearest dollar
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.
Larger wants to take a trip in 8 years. She needs 2,400$. How much should she deposit
into an account that pay 3.5% interest daily to meet her goal, round to nearest dollar
~~~~~~~~~~~~~~~~~~~~ 

Write an equation for the future value of the deposit X in 8 years, compounded daily


    X%2A%281%2B0.035%2F365%29%5E%288%2A365%29 = 2400


Find X

    X = 2400%2F%281%2B0.035%2F365%29%5E%288%2A365%29 =  1814  dollars  (rounded).    ANSWER

Solved.

---------------------

To see many other similar  (and different)  solved problems on compounded interest accounts,  look into the lesson
    - Compounded interest percentage problems
in this site.

Learn the subject from there.


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                        A T T E N T I O N   ( ! )


Tutor @MathTherapy  MISREAD  the problem.

In this problem,  the account is  NOT  an annuity,  so the solution by @MathTherapy is  IRRELEVANT.

From the text,  it is clear that this account is one-time deposit, compounded daily.

So,  my solution is correct,  while the  @MathTherapy' solution is irrelevant.



Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Larger wants to take a trip in 8 years. She needs 2,400$. How much should she deposit into an account that pay 3.5% interest daily to meet her goal, round to nearest dollar

The formula for an ORDINARY ANNUITY need to be used here. This is:
matrix%281%2C3%2C+FV%5Boa%5D%2C+%22=%22%2C+PMT%28%28%281+%2B+r%29%5En+-+1%29%2Fr%29%29, or matrix%281%2C3%2C+PMT%2C+%22=%22%2C+FV%5Boa%5D%2F%28%28%281+%2B+r%29%5En+-+1%29%2Fr%29%29, or matrix%281%2C3%2C+PMT%2C+%22=%22%2C+FV%5Boa%5D%28r%2F%28%281+%2B+r%29%5En+-+1%29%29%29, where: 
 PMT = PAYMENT/DEPOSIT to be made throughout the investment period annuity (UNKNOWN, in this case)
FVoa = FUTURE VALUE of the annuity ($2,400, in this case)
   r = interest RATE, per period(matrix%281%2C3%2C+.035%2F360%2C+or%2C+.007%2F72%29, in this case) <=== Note that 360 is NORMALLY used
                                                                     to represent the number of days
                                                                     in a year. 365 can also be used.
   n = total NUMBER of investment periods (8 * 360 = 2,880, in this case)

matrix%281%2C3%2C+PMT%2C+%22=%22%2C+FV%5Boa%5D%28r%2F%28%281+%2B+r%29%5En+-+1%29%29%29
 ---- Substituting $2,400 for FVoa, .007%2F72 for r, and 2,880 for n

Payment/Amount to be made/deposited, daily , or PMT = 0.722144255, rounded to $0.72.


SIDE NOTE:
A deposit of $0.72 per day for 360 days per year, at a matrix%281%2C3%2C+.007%2F72%2C+per%2C+day%29 (3.5% annual) interest rate, for 2,880 days
(8 years) = $2,392.87, which falls SHORT of her $2,400 goal by $7.13 ($2,400 - $2,392.87). However, a daily deposit
of $0.722144, rounded from $0.722144255, will certainly HIT the $2,400 MARK.

Another SIDE NOTE:
Above, I rounded off to the NEAREST cent, not nearest DOLLAR. So, in reality, rounding off $0.72244255 to the nearest
DOLLAR gives us $1, per day, which will be more than enough to reach her TARGET of $2,400 in 8 years, or 2.880 days. As
a matter of fact, $1 per day will yield $3,323.44 in 8 years (2,880 days), $923.44 more than her target goal of $2,400.

SELAH!!