Charlie wants to buy a $900 TV in 9 months. How much should he invest now at 17% simple interest to have the money in 9 months?
9 months is .75 years
so interest % is 17*.75 = 12.75%
900 = 1.1275 x
x = 900/1.1275
To determine how much Charlie should invest now, we need to calculate the principal amount using the formula for simple interest:
Interest = Principal * Rate * Time
In this case, the interest is equal to the price of the TV minus the principal amount (since the interest is how much he will earn on his investment to reach the desired amount). Rearranging the formula, we get:
Principal = Price of TV - (Interest / Rate * Time)
Let's calculate the interest first:
Interest = $900 TV price - Principal
Now, we know that the interest is calculated at a rate of 17% per year for a time period of 9 months. However, the interest rate needs to be converted to a decimal and the time period to years to match the units:
Rate = 17% = 0.17
Time = 9 months = 9/12 years = 0.75 years
Now, we can substitute the values into the formula and solve for the principal:
Interest = Principal * Rate * Time
$900 - Principal = Principal * 0.17 * 0.75
$900 - Principal = 0.1275 * Principal
$900 = 1.1275 * Principal
Principal = $900 / 1.1275
Principal ≈ $797.76
Therefore, Charlie should invest approximately $797.76 now at a 17% simple interest rate to have the money to buy the $900 TV in 9 months.