Homer won a prize in the lottery of $1000, payable $500 immediately and $500 plus 4% simple interest payable in 250 days. Getting impatient, Homer sells the promissory note to Moe for $450 cash after 130 days. Using a nominal 360 day year, find the simple interest rate, rounded to .01, earned by Moe.
To find the simple interest rate earned by Moe, we'll first calculate the total amount Moe received from buying the promissory note from Homer.
Homer received $500 immediately and $500 plus 4% simple interest payable in 250 days. Since Moe bought the promissory note after 130 days, the amount payable would have accumulated interest for 120 days (250 - 130).
The interest accrued in these 120 days can be calculated using the formula:
Interest = Principal x Rate x Time
Where:
Principal = $500
Time = 120 days
To find the interest rate, we use the formula:
Rate = (Interest / Principal) x (360 / Time)
Substituting the given values, we have:
Rate = (Interest / $500) x (360 / 120)
Now, let's calculate the interest using the principal and time:
Interest = Principal x Rate x Time
Interest = $500 x Rate x 120
To find the interest rate, we rearrange the formula:
Rate = (Interest / Principal) x (360 / Time)
Plugging in the given values:
Rate = (Interest / $500) x (360 / 120)
Rate = (Interest / $500) x 3
Now, let's calculate the interest:
Interest = $500 x Rate x 120
Substituting the given values:
$450 = $500 + Interest
Solving for Interest:
Interest = $450 - $500
Interest = -$50
Since the interest is negative, it means Moe paid less than what he should have received, resulting in a loss. Therefore, Moe did not earn any interest in this transaction.
In conclusion, Moe did not earn any interest from buying the promissory note from Homer.