Assume a three-month CD purchased for $3000 pays simple interest at an annual rate of 10%. What is the balance at maturity? I don't have any work. This is question one and I have 19 more. I don't understand how to arrive at the answer.
Ah, CDs, the financial equivalent of "I'll love you back after a certain amount of time". Let me help you out with this one.
So, you have a three-month CD purchased for $3000 that pays simple interest at an annual rate of 10%. To find the balance at maturity, we need to calculate the interest earned.
First, we convert the annual rate of 10% to a quarterly rate. Since there are four quarters in a year, the quarterly rate is 10% divided by 4, which is 2.5%.
Next, we calculate the interest earned for three months. Simple interest is calculated by multiplying the principal (which is $3000) by the interest rate (which is 2.5%) and the time period (which is 3 months divided by 12 to get the quarter equivalent). So the interest earned is:
Interest = $3000 * 2.5% * (3/12) = $18.75
Finally, we add the interest earned to the principal to find the balance at maturity:
Balance at maturity = $3000 + $18.75 = $3018.75
So, the balance at maturity will be $3018.75. And remember, the only clowns we want to see are the ones in the circus, not in our financial statements!
To calculate the balance at maturity for a CD, we can use the formula for simple interest:
Interest = Principal × Interest Rate × Time
Let's break down the information given in the question:
Principal (P) = $3000
Interest Rate (R) = 10% per year = 0.1 (in decimal form)
Time (T) = 3 months = 3/12 years (since the interest rate is given as an annual rate)
Now we can substitute these values into the formula:
Interest = $3000 × 0.1 × 3/12
Simplifying the calculation:
Interest = $3000 × 0.1 × 1/4
Interest = $3000 × 0.025
Interest = $75
The interest earned on the CD is $75. To find the balance at maturity, we need to add the interest to the principal:
Balance at maturity = Principal + Interest
Balance at maturity = $3000 + $75
Balance at maturity = $3075
Therefore, the balance at maturity for the three-month CD would be $3075.
To find the balance at maturity, you need to calculate the amount of interest earned and add it to the principal amount.
In this case, the principal amount (the amount you initially invested) is $3000.
To calculate the amount of interest earned, you need to multiply the principal amount by the interest rate for the given period, which is 10% annual rate for three months.
First, convert the annual interest rate to a quarterly rate by dividing it by 4 (since there are 4 quarters in a year):
Quarterly interest rate = 10% / 4 = 0.10 / 4 = 0.025
Now, calculate the interest earned over the three-month period by multiplying the quarterly interest rate by the principal amount:
Interest earned = $3000 * 0.025 = $75
Finally, add the interest earned to the principal amount to find the balance at maturity:
Balance at maturity = $3000 + $75 = $3075
Therefore, the balance at maturity for the three-month CD purchased for $3000 with a 10% annual interest rate is $3075.
P = Po + Po*r*t
P = 3,000 + 3000*(0.10/12)*3 = $3,075.