SOLUTION: Just here to check my answers if am I correct. Its gonna be a long question anyway If Im correct no need for solutions, if wrong, well just show the solution and right answer. Ru

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Just here to check my answers if am I correct. Its gonna be a long question anyway If Im correct no need for solutions, if wrong, well just show the solution and right answer. Ru      Log On


   

Question 909166: Just here to check my answers if am I correct. Its gonna be a long question anyway
If Im correct no need for solutions, if wrong, well just show the solution and right answer.
Rules:
log answer in 6 decimal places(no round-off error, just copy)
Money( with 2 decimal place, round-off error)
The Villager of Kieler completes an exploratory study and find the current village tower will need a replacement in 10 years at a cost of $290,000. To finance this amount, the village board will at this time asses it's 958 homeowners with a one time surcharge and then invest this amount in a 10 year Cash Deposit paying 8.25% interest compounded semiannually.
a.How much will the village of Kieler need to invest at this time in this CD in order to raise the $290,000 in 10 years?
b.What amount should each homeowner pay as a surcharge?
Answers:
a.$129,210.26
b.$134.88
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Ten years at two compoundings per year is 20 compounding periods of time. The initial investment quantity is unknown and can be solved. Call this a.

290000=a%2A%281.085%29%5E20, not using a Natural Log model (although it could be used instead).

The rate is used as 1+0.085, as a decimal number.

log%2810%2C290000%29=log%2810%2Ca%29%2Blog%2810%2C1.085%5E20%29
log%2810%2C290000%29=log%2810%2Ca%29%2B20%2Alog%2810%2C1.085%29
log%2810%2Ca%29=log%2810%2C290000%29-20%2Alog%2810%2C1.85%29
log%2810%2Ca%29=5.4624%2B20%2A0.0354297
log%2810%2Ca%29=5.4624-0.7086
log%2810%2Ca%29=4.7538
highlight%28a=56728.33%29-----The amount to invest.

Each person of the village, of 958 people, would pay a%2F958 dollars, or
a=56728.33%2F958=highlight%2859.22%29 dollars each.

My calculations may not have used the accuracy specified in the problem description. Precision might be off a little bit. software calculator was used; not a table of logarithms.

Try checking:
56728%2A1.085%5E20=289996, not too far from 290000.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Just here to check my answers if am I correct. Its gonna be a long question anyway
If Im correct no need for solutions, if wrong, well just show the solution and right answer.
Rules:
log answer in 6 decimal places(no round-off error, just copy)
Money( with 2 decimal place, round-off error)
The Villager of Kieler completes an exploratory study and find the current village tower will need a replacement in 10 years at a cost of $290,000. To finance this amount, the village board will at this time asses it's 958 homeowners with a one time surcharge and then invest this amount in a 10 year Cash Deposit paying 8.25% interest compounded semiannually.
a.How much will the village of Kieler need to invest at this time in this CD in order to raise the $290,000 in 10 years?
b.What amount should each homeowner pay as a surcharge?
Answers:
a.$129,210.26
b.$134.88


With P being the present value, we get: log+P+=+log+%28290000%2F1.04125%5E20%29_____P+=+290000%2F1.04125%5E20

Your answer is correct!! The village needs to invest that amount (present value) to raise the $290,000 (future value),

in 10 years. However, I got $highlight_green%28129210.471006%29 (to 6 decimal places), and $highlight_green%28129210.47%29 (rounded to 2 decimal places)

- a difference of just a few cents, maybe caused by rounding. My per-person calculation is exactly what you have.



Good job!!