I have $128 in my savings account. The bank pays me 3.1% annual interest. If I do not deposit or withdraw any money from the account, after how many years will my account balance first exceed $280? I would love some help on this! THANKS! =]
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The amount in the account is, after...
1 year: A_1 = 128 + 0.031(128) = 1.031(128)
2 years: A_2 = 1. 031^2(128)
...
n years: A_n = 1.031^n(128)
Then for A_n = 280 we have:
1.031^n(128) = 280
=> n*ln(1.031) = ln(280/128)
=> n = ln(280/128)/ln(1.031) = 25.6
So, since n has to be a whole number when n=26 years later you have at least $280 in the account. (or more precisely 1.031^(26)*(128) = $283.10 after 26 years)
1 year: A_1 = 128 + 0.031(128) = 1.031(128)
2 years: A_2 = 1. 031^2(128)
...
n years: A_n = 1.031^n(128)
Then for A_n = 280 we have:
1.031^n(128) = 280
=> n*ln(1.031) = ln(280/128)
=> n = ln(280/128)/ln(1.031) = 25.6
So, since n has to be a whole number when n=26 years later you have at least $280 in the account. (or more precisely 1.031^(26)*(128) = $283.10 after 26 years)
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280 = 128(1.031)^y
Take logs
log(280) = log(128) + y(log1.031)
Then solve for y and put numbers in from the calculator for the logs and calculate the answer.
Take logs
log(280) = log(128) + y(log1.031)
Then solve for y and put numbers in from the calculator for the logs and calculate the answer.