SOLUTION: If you deposit P dollars into a bank account paying an annual interest rate r, (expressed as a decimal), with n interest ayments each year, the amount A you would have after t year

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: If you deposit P dollars into a bank account paying an annual interest rate r, (expressed as a decimal), with n interest ayments each year, the amount A you would have after t year      Log On


   

Question 178415: If you deposit P dollars into a bank account paying an annual interest rate r, (expressed as a decimal), with n interest ayments each year, the amount A you would have after t years is A = P(1= r/n)^nt. Marta places $100 in a savings account earning 2% annual interest, compounded quarterly.
If Marta adds no more money to the account, how long will it take the money in the account to reach $125?
How long will it take for MArta's momey to double?
Answer by EMStelley(208) About Me  (Show Source):
You can put this solution on YOUR website!
Ok, so we know that P=100, r=0.02, n=4 and we want A=125. So the question is to solve for t.
125=100%281%2B0.02%2F4%29%5E%284t%29
The first thing I will do is divide both sides by 100.
1.25=%281%2B0.005%29%5E%284t%29
Now, since the variable is an exponent, we need to use logarithms so we can get the exponent down. So I will take the log of both sides.
log%281.25%29=log%281.005%5E%284t%29%29
log%281.25%29=4tlog%281.005%29
So,
t=log%281.25%29%2F4log%281.005%29
Thus,
t=11.185
So, depending on how you are supposed to round, it will take her 11.2 years to reach $125, or if you are supposed to round to the year, it would be 12 years. Now, for doubling, that would mean we want A=200. So you do the same exact steps with A=200 instead of 125.