Charlie wants to buy a $500 TV in 9 months. How much should he invest now at 8% simple interest to have the money in 9 months?
P = Po + Po*r*t = 500
Po + Po*(0.08/12)*9 = 500
Po + 0.06Po = 500
1.06Po = 500
Po = $471.70
To find out how much Charlie should invest now at 8% simple interest to have $500 in 9 months, we need to use the formula for simple interest:
Simple Interest = Principal (P) * Rate (R) * Time (T)
First, we need to rearrange the formula to solve for the Principal (P):
Principal (P) = Simple Interest / (Rate (R) * Time (T))
In this case, we know that the simple interest Charlie wants to earn is $500 and the rate is 8% (expressed as a decimal, 0.08). The time is 9 months.
Plugging the values into the formula:
Principal (P) = $500 / (0.08 * 9/12)
To calculate this, we need to convert 9 months to years by dividing by 12.
Principal (P) = $500 / (0.08 * 0.75)
Now, we can multiply the rate and time:
Principal (P) = $500 / 0.06
Finally, dividing $500 by 0.06, we find:
Principal (P) = $8,333.33
Therefore, Charlie should invest approximately $8,333.33 at 8% simple interest to have $500 in 9 months.