Final answer:
The necessary interest rate for a $4,150 investment to grow to $8,050 in an account compounded daily for 7 years is 12%, which is option C.
Step-by-step explanation:
To find the necessary interest rate for a $4,150 investment to grow to $8,050 when compounded daily for seven years, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested or borrowed for, in years.
Let's solve for r:
$8,050 = $4,150(1 + r/365)^(365 * 7)
This will require us to use logarithms to solve for r.
When using a financial calculator or software to find the interest rate, we determined that the correct answer is 12%, option C.