Final answer:
It will take approximately 6 years for $3100 to grow into $4395.65 at a 3.2% annual interest rate compounded annually.
Step-by-step explanation:
To find out how long it will take for $3100 to grow into $4395.65 with a 3.2% annual interest rate compounded annually, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
- A is the final amount ($4395.65)
- P is the starting principal ($3100)
- r is the annual interest rate (3.2% as a decimal, or 0.032)
- n is the number of times interest is compounded per year (in this case, once)
- t is the number of years
Let's solve for t by rearranging the formula:
$4395.65 = $3100(1 + 0.032/1)^(1*t)
Simplifying:
$4395.65 = $3100(1.032)^t
Dividing both sides by $3100:
(1.4165) = (1.032)^t
Now we need to solve for t. We can use logarithms for this. Taking the logarithm (base 1.032) of both sides:
log(1.4165) / log(1.032) = t
Using a calculator, we find that t ≈ 6.
Therefore, it will take approximately 6 years for $3100 to grow into $4395.65 at a 3.2% annual interest rate compounded annually.