Assume a 30 month CD purchased for 2000 pay simple interest at an annual rate of 5.5%. How much total interest does it turn what is the balance at maturity.
They want to know the total interest and the balance at maturity and they want us to give our answer to two decimal places
I = PRT
I = 2000 * 0.055 * 2.5
I = ?
Add the interest to the principle to get the balance.
To calculate the total interest earned, we can use the formula:
Total Interest = Principal × Interest Rate × Time
In this case, the principal (P) is $2000, the interest rate (R) is 5.5% (or 0.055 as a decimal), and the time (T) is 30 months (or 2.5 years).
Total Interest = $2000 × 0.055 × 2.5 = $275
So, the total interest earned is $275.
To determine the balance at maturity, we need to add the total interest to the principal amount.
Balance at Maturity = Principal + Total Interest
Balance at Maturity = $2000 + $275 = $2275
Therefore, the balance at maturity is $2275.
To calculate the total interest and the balance at maturity for a 30-month CD with an annual interest rate of 5.5%, we need to follow the steps below:
Step 1: Determine the interest rate per period.
Since the CD has an annual interest rate, we need to calculate the interest rate per period by dividing the annual rate by the number of periods in a year. In this case, the CD is for 30 months, so the number of periods in a year is 12 since there are 12 months in a year. Therefore, the interest rate per period is (5.5% / 12) = 0.4583333% (rounded to seven decimal places).
Step 2: Calculate the total interest earned.
To find the total interest earned, we multiply the principal amount by the interest rate per period and by the number of periods. In this case, the principal amount is $2000, the interest rate per period is 0.4583333%, and the number of periods is 30. Thus, the total interest earned is ($2000 * 0.4583333% * 30) = $275 (rounded to the nearest dollar).
Step 3: Calculate the balance at maturity.
The balance at maturity is equal to the principal amount plus the total interest earned. In this case, the principal amount is $2000, and the total interest earned is $275. Therefore, the balance at maturity is ($2000 + $275) = $2275.
So, the total interest earned is $275, and the balance at maturity is $2275.