2. Dr. Enriquez borrowed $6,370 from the National Bank of Belize at 7.25 per cent per annum simple interest for 6 months. Calculate:
a) The simple interest Dr. Enriquez paid the bank for the money she borrowed.
b) The total amount of money that was repaid to the bank.
c) The amount of each monthly installment.
a) The simple interest Dr. Enriquez paid the bank can be calculated using the formula:
Interest = Principal x Rate x Time
In this case, the principal (P) is $6,370, the interest rate (R) is 7.25% per annum, and the time (T) is 6 months.
Converting the interest rate to a decimal: R = 7.25% / 100 = 0.0725
Converting the time to years: T = 6 months / 12 months = 0.5 years
Now we can calculate the interest:
Interest = $6,370 x 0.0725 x 0.5 = $183.62
Therefore, Dr. Enriquez paid $183.62 in simple interest to the bank.
b) The total amount of money repaid to the bank is calculated by adding the principal and the interest:
Total = Principal + Interest
Total = $6,370 + $183.62 = $6,553.62
Therefore, the total amount of money repaid to the bank is $6,553.62.
c) The amount of each monthly installment can be calculated by dividing the total amount repaid by the number of months:
Monthly Installment = Total Amount / Number of Months
In this case, we have 6 months, so
Monthly Installment = $6,553.62 / 6 = $1,092.27
Therefore, the amount of each monthly installment is $1,092.27.
To calculate the simple interest Dr. Enriquez paid, we can use the formula:
Simple Interest = Principal * Rate * Time
a) The principal amount Dr. Enriquez borrowed is $6,370.
The annual interest rate is 7.25% or 0.0725 as a decimal.
The time period is 6 months or 0.5 years.
Plugging in these values into the formula:
Simple Interest = $6,370 * 0.0725 * 0.5 = $231.06
Therefore, the simple interest Dr. Enriquez paid the bank is $231.06.
b) To calculate the total amount repaid to the bank, we need to add the principal amount to the simple interest:
Total Amount Repaid = Principal + Simple Interest
Total Amount Repaid = $6,370 + $231.06 = $6,601.06
Therefore, the total amount repaid to the bank is $6,601.06.
c) To find the amount of each monthly installment, we divide the total amount repaid by the number of months, which is 6:
Monthly Installment = Total Amount Repaid / Number of Months
Monthly Installment = $6,601.06 / 6 = $1,100.18 (rounded to two decimal places)
Therefore, the amount of each monthly installment is approximately $1,100.18.