Final answer:
The short-term investment of $27,350 made on September 30 will be worth $27,529.89 at maturity after 200 days, earning 1.2% per annum interest.
Step-by-step explanation:
On September 30, an inn made a short-term investment of $27,350 at an interest rate of 1.2% per annum for a period of 200 days. To find out how much this investment will be worth at maturity, we need to calculate the interest earned during this period and add it to the original investment.
The formula to calculate simple interest is: Interest = Principal × Rate × Time. In this case, the principal is $27,350, the rate is 1.2%/365 days (since the interest rate given is an annual rate and we need to adjust it for 200 days), and the time is 200/365 year (since there are 365 days in a year).
Interest = $27,350 × (1.2/100) × (200/365)
Interest = $27,350 × 0.012 × 0.54794520548
Interest = $179.89 (rounded to two decimal places)
Now, add the interest to the initial investment to find the value at maturity:
Value at Maturity = Principal + Interest
Value at Maturity = $27,350 + $179.89
Value at Maturity = $27,529.89
Therefore, the investment will be worth $27,529.89 at maturity.