SOLUTION: 1. You have deposited $7,000 in an account that pays 6.25% interest compounded continuously. How long will it take your money to double? 2. You have deposited $12,000 in an

Question 929310: 1. You have deposited $7,000 in an account that pays 6.25% interest compounded continuously. How long will it take your money to double?

2. You have deposited $12,000 in an account compounded monthly. After 7 years the balance has grown to $15,532. Find the rate.

PLEASE HELP ME ANSWER THESE 2 QUESTIONS!!!
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
1. For continuous compounding, the balance amount is related to
the principal (initial investment ,
the rate (written as a decimal), and
the time in years, , by the formula
.
The number is an irrational number like that come up pretty often . It is not invented to make students learn one more number; it just comes up naturally.
We use it as a base for powers, and of course for logarithms that we call natural logarithms

So, for , , and , we can write
--->
Note that we did not need to know the amount invested.
---> (taking natural logarithms on both sides).
Using the approximate value ,
-->--> (rounded).
So, it will take 11 years for the money to double.
2. $12,000 compounded monthly. After 7 years the balance has grown to $15,532. Find the rate.
For monthly compounding, the balance grow by of the yearly rate every month.
So over , the balance grew by a factor of applied times to
.
Solving for rate:

Using logarithm base 10 for an approximate calculation:

Reversing the logarithm by calculating power of 10 on both sides of the equal sign:

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