SOLUTION: I posted this question twice earlier with no response. Would appreciate your help. Antonio’s bank charges an $8 service fee each month if his account goes below $500. In June,

Question 1137698: I posted this question twice earlier with no response. Would appreciate your help.
Antonio’s bank charges an $8 service fee each month if his account goes below $500. In June, Antonio had $510 in his account. He withdrew $25 and then did not have any transactions in his account for 6 months.
a. Write as an integer the amount by which Antonio’s bank balance changed during the six months.
b.What was the balance in the account at the end of January?
c. How much will Antonio have to deposit for his account to be at least $500?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
in june, antonio has 510 in his account.

he withdrew 25 dollars and didn't have any other transactions for 6 months.

in june, his account went from 510 to 485.

unless his account was earning some interest, it would remain at that level forever.

you didn't give an interest rate that the account was earning at.

for example, if the account was earning 12% per year compounded monthly, then the account would be earning 1% per month and the figures would be as follows:

f = p * (1 + r) ^ n is the formula to use for this.

f is the future value
p is the preswent value
r is the interest rate per time period
n is the number of time periods.

since you are going month by month, you only need the interest rate per month and you would do the following.

in june, his balance was 485 after the 25 dollar withdrawal.

at the end of june, he paid 8 dollars because the account was less than 500.

at the end of july, the account grew to 1.01 * 485 = 489.85 which is still less than 500, so he paid an 8 dollar transaction fee.

at the end of august, the account grew to 1.01 * 489.85 = 494.7485 which is still less than 500, so he paid an 8 dollar transaction fee.

at the end of september, the account grew to 1.01 * 494.7485 = 499.695985 which is still less than 500, so he paid an 8 dollar transaction fee.

at the end of october, the account grew to 1.01 * 499.695985 = 504.6929449 which is more than 500, so he didn't have to pay the 8 dollar transaction fee any more as long as the account balance remained above 500.

the 1% per month is very generous, since most bank accounts don't give 12% interest rate per year.

it's more like 1.2 or 2.4 percent per year which would be .1 or .2 percent per month.

i used those number because they divide evenly, not because those are the actual percentages the bank might give you.

you can use the formula provided to see when the account would go past 500.

the formula is f = p * (1 + r) ^ n

f is the future value, which you would set at 500.

p is the present value which you would set at 485.

r is the interest rate per time period which is the annual interest rate / 12.

to get the monthly rate, you divide the annual percent rate by 1200.

12 to get it to the month and 100 to get it to a rate rather than a percent rate.

n is the number of months.

at 12% percent interest rate per year, the interest rate per month is 12/1200 = .01 and the formula becomes 500 = 485 * (1 + .01) ^ n.

at 1.2 percent interest rate per year, the interest rate per month is 1.2/1200 = .001 and the formula becomes 500 = 485 * (1 + .001) ^ n.

at 2.4 percent interest rate per year, the interest rate per month is 2.4/1200 = .0024 and the formula becomes 500 = 485 * (1 + .002) ^ n.

you would solve for n in these formulas.

i'll show you how to do one and you can do the others if you want to.

i'll give you the answers for all.

at 12%, the formula is 500 = 485 * (1 + .01) ^ n

divide both sides of this formula by 485 and simplify to get 500/485 = 1.01 ^ n

take the log of both sides of this formula to get log(500/485) = log(1.01^n)

since log (1.01^n) is equal to n * log(1.01), the formula becomes log(500/485) = n * log(1.01)

divide both sides of this equation by log(1.01) to get log(500/485) / log(1.01) = n

solve for n to get n = 3.061125096.

the future value will be 500 in 3.061125096 months.

starting from end of june, that becomes end of july is 1 month from end of june, end of august is 2 months from end of june, end of september is 3 months from end of june. that means the account balance will become 500 some time in october.

we already did that above and the answer in both cases agree with each other, as they should.

that's at 12% per year.

at 1.2% per year and 2.4% per year, i calculated how long it would take the the account to get to 500.

at 1.2% per year, it would take 30.47443455 months for the account to grow to 500.

at 2.4% per year, it would take 15.24482827 months for the account to grow to 500.

use the formula i provided you and substitute your percent interest rate per year by that rate / 1200 and put it in the formula and solve as i did using logs (assuming you know how to do logs).

in fact, assuming you know how to do logs, you can just do the following.

take log(500/485) / log(x) to get the number of months.

x would be your annual interest rate / 1200 + 1.

at 12%, x would be equal to 12/1200 + 1 which would become x = 1.01.

at 1.2%, x would be equal to 1.2/1200 + 1 which would become x = 1.001.

at 2.4%, x would be equal to 2.4/1200 + 1 which would become x = 1.002

do the same with whatever percent interest rate per year you have and you'll get the numbe of months it takes for the acount to become equal to 500 again.

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

I posted this question twice earlier with no response. Would appreciate your help.
Antonio’s bank charges an $8 service fee each month if his account goes below $500. In June, Antonio had $510 in his account. He withdrew $25 and then did not have any transactions in his account for 6 months.
a. Write as an integer the amount by which Antonio’s bank balance changed during the six months.
b.What was the balance in the account at the end of January?
c. How much will Antonio have to deposit for his account to be at least $500?

@THEO's response is very, very WRONG! He needs to READ the problem, jut like anyone who's helping a person with math, would tell he/she.
First of all, his balance at the end of June is NOT $485. AGAIN, READ THE ENTIRE PROBLEM, @THEO, and then try again, if you want to help.
And please, don't tell the student anything about INTEREST as this most definitely is not a factor in the POSTED problem.
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