Final answer:
To achieve an additional $550 from a $1,000 investment at 7% simple interest, it would take approximately 7 full years and 313 days. This is calculated using the simple interest formula I = PRT where I is the interest, P is the principal, R is the interest rate, and T is time.
Step-by-step explanation:
Calculating Time to Achieve Investment Goal with Simple Interest
To calculate the time necessary to achieve an investment goal using simple interest, you can use the formula I = PRT, where I is the interest earned, P is the principal amount, R is the rate of interest, and T is the time in years. In this case, the student is looking to find out how long it will take for a $1,000 investment at 7% simple interest to increase by $550 through interest alone.
To solve this, first calculate the interest needed to reach the investment goal and then rearrange the formula to solve for time (T):
I = PRT
$550 = $1,000 × 0.07 × T
T = $550 / ($1,000 × 0.07)
T = $550 / $70
T = 7.857 years
To convert years into the total number of full years and the remaining days, consider that 1 year is equivalent to 365 days:
0.857 years × 365 days/year = 313 days
So, it would take 7 full years and 313 days to reach the investment goal of an additional $550 using simple interest.