Gina loaned Gerry $300 at an interest rate of 10 percent a year. How much interest will Gina get if Gerry pays Gina after 6 months?(1 point)
To calculate the interest, we need to first determine the interest for a full year, and then divide it by 2 to get the interest for 6 months.
Interest for a full year: $300 * 0.10 = $30
Interest for 6 months: $30 / 2 = $<<30/2=15>>15
Therefore, Gina will get $15 in interest if Gerry pays after 6 months.
Apologies for the confusion. The "2" is used to calculate the interest for 6 months instead of a full year. Since 6 months is half of a year, we divide the interest for a full year by 2 to determine the interest for 6 months.
Calculate the simple interest on a $100,000 investment at an interest rate of 12 percent a year after 6 months.(1 point)
To calculate the simple interest, we will use the formula:
Simple Interest = Principal * Rate * Time
Here, the Principal is $100,000, the Rate is 12% (0.12 as a decimal), and the Time is 6 months (0.5 years).
Simple Interest = $100,000 * 0.12 * 0.5
Simple Interest = $6,000
Therefore, the simple interest on a $100,000 investment at an interest rate of 12% a year after 6 months is $6,000.
Find the value after five years of a $3,000 savings account that pays 3% interest compounded yearly. Round the answer to two decimal places.(1 point)
To calculate the value after five years with yearly compounding, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount ($3,000)
r = the annual interest rate (3% or 0.03 as a decimal)
n = the number of times interest is compounded per year (1 for yearly compounding)
t = the number of years (5 years)
Plugging in the values:
A = $3,000(1 + 0.03/1)^(1*5)
A = $3,000(1.03)^5
A = $3,000(1.159274)
A ≈ $3,477.82
Therefore, the value after five years of a $3,000 savings account that pays 3% interest compounded yearly is approximately $3,477.82.
use the P(1+r)^t formula
Apologies for the confusion. You are correct. To calculate the value using the P(1 + r)^t formula, we can directly plug in the values:
A = P(1 + r)^t
A = $3,000(1 + 0.03)^5
Calculating:
A ≈ $3,000(1.03)^5
A ≈ $3,000(1.159274)
A ≈ $3,477.82
Therefore, the value after five years of a $3,000 savings account that pays 3% interest compounded yearly is approximately $3,477.82.
Find the balance after 10 years of a $30,000 savings account that pays 10% interest compounded yearly.
To find the balance after 10 years with yearly compounding, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (balance)
P = the principal amount ($30,000)
r = the annual interest rate (10% or 0.10 as a decimal)
n = the number of times interest is compounded per year (1 for yearly compounding)
t = the number of years (10 years)
Plugging in the values:
A = $30,000(1 + 0.10/1)^(1*10)
A = $30,000(1.10)^10
Calculating:
A ≈ $30,000(2.59374)
A ≈ $77,812.14
Therefore, the balance after 10 years of a $30,000 savings account that pays 10% interest compounded yearly is approximately $77,812.14.