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.
Between simple interest at 8% and compound interest at 9%, find the higher resulting balance after investing $500 for a period of 10 years. Round the answer to two decimal places.(1 point)
The higher resulting balance after investing $500 for a period of 10 years is $
.
To determine the higher resulting balance after investing $500 for 10 years, we can calculate the balances using both simple interest at 8% and compound interest at 9%.
Simple Interest:
Simple Interest = Principal * Rate * Time
Simple Interest = $500 * 0.08 * 10
Simple Interest = $400
Compound Interest:
Compound Interest = Principal * (1 + Rate)^Time - Principal
Compound Interest = $500 * (1 + 0.09)^10 - $500
Compound Interest ≈ $951.56
Therefore, the higher resulting balance after investing $500 for a period of 10 years is approximately $951.56, which is obtained with compound interest at 9%.
Aria is investing $6,700 of her savings from her summer job for her college fund. She is planning to invest the amount for 3 years and can choose between simple interest at 6.5% and compound interest at 6%. Find the difference between the two interest earning types to help Aria decide which investing option is best for her.(1 point)
Responses
Aria should invest with 6.5% simple interest because it will result in $26.69 more in interest earnings.
Aria should invest with 6.5% simple interest because it will result in $26.69 more in interest earnings.
Aria should invest with 6.5% simple interest because it will result in $187.26 more in interest earnings.
Aria should invest with 6.5% simple interest because it will result in $187.26 more in interest earnings.
Aria should invest with 6% compound interest because it will result in $86.76 more in interest earnings.
Aria should invest with 6% compound interest because it will result in $86.76 more in interest earnings.
Aria should invest with 6% compound interest because it will result in $73.81 more in interest earnings.
use the P(1+r)^t formula
Apologies for the previous response. Let's calculate the interest using the formula P(1 + r)^t for both simple interest at 6.5% and compound interest at 6%.
For Simple Interest:
Principal (P) = $6,700
Rate (r) = 0.065 (6.5% as a decimal)
Time (t) = 3 years
Simple Interest = P * r * t
Simple Interest = $6,700 * 0.065 * 3
Simple Interest ≈ $1,302.50
For Compound Interest:
Principal (P) = $6,700
Rate (r) = 0.06 (6% as a decimal)
Time (t) = 3 years
Compound Interest = P * (1 + r)^t - P
Compound Interest = $6,700 * (1 + 0.06)^3 - $6,700
Compound Interest ≈ $1,215.74
The difference in interest earning is:
$1,302.50 - $1,215.74 = $86.76
Therefore, the difference between the two interest earning types is $86.76. Hence, Aria should invest with 6.5% simple interest because it will result in $86.76 more in interest earnings compared to compound interest at 6%.
thats not an option
Apologies for the confusion. Let's recalculate the difference between the two interest earning types using the formula P(1 + r)^t as requested.
For Simple Interest:
Principal (P) = $6,700
Rate (r) = 0.065 (6.5% as a decimal)
Time (t) = 3 years
Simple Interest = P * r * t
Simple Interest = $6,700 * 0.065 * 3
Simple Interest ≈ $1,302.50
For Compound Interest:
Principal (P) = $6,700
Rate (r) = 0.06 (6% as a decimal)
Time (t) = 3 years
Compound Interest = P * (1 + r)^t - P
Compound Interest = $6,700 * (1 + 0.06)^3 - $6,700
Compound Interest ≈ $6,700 * (1.06)^3 - $6,700
Compound Interest ≈ $7,178.34 - $6,700
Compound Interest ≈ $478.34
The difference in interest earning is:
$1,302.50 - $478.34 = $824.16
Therefore, the difference between the two interest earning types is $824.16. Hence, Aria should invest with the 6.5% simple interest because it will result in $824.16 more in interest earnings compared to the compound interest at 6%.
choose one of the options:Aria should invest with 6.5% simple interest because it will result in $26.69 more in interest earnings.
Aria should invest with 6.5% simple interest because it will result in $26.69 more in interest earnings.
Aria should invest with 6.5% simple interest because it will result in $187.26 more in interest earnings.
Aria should invest with 6.5% simple interest because it will result in $187.26 more in interest earnings.
Aria should invest with 6% compound interest because it will result in $86.76 more in interest earnings.
Aria should invest with 6% compound interest because it will result in $86.76 more in interest earnings.
Aria should invest with 6% compound interest because it will result in $73.81 more in interest earnings.
Apologies for the confusion caused. Let's recalculate the difference between the two interest earning types.
For Simple Interest:
Principal (P) = $6,700
Rate (r) = 0.065 (6.5% as a decimal)
Time (t) = 3 years
Simple Interest = P * r * t
Simple Interest = $6,700 * 0.065 * 3
Simple Interest = $1,302.50
For Compound Interest:
Principal (P) = $6,700
Rate (r) = 0.06 (6% as a decimal)
Time (t) = 3 years
Compound Interest = P * (1 + r)^t - P
Compound Interest = $6,700 * (1 + 0.06)^3 - $6,700
Compound Interest ≈ $7,178.34 - $6,700
Compound Interest ≈ $478.34
The difference in interest earning is:
$1,302.50 - $478.34 = $824.16
Therefore, Aria should invest with 6.5% simple interest because it will result in $824.16 more in interest earnings compared to compound interest at 6%.
Analyze the incentive as shown here to find the total price when two medium one-topping pizzas are purchased with the incentive.
“1 one-topping medium pizza for $7.99 or 2 one-topping medium pizzas for $6.49 each.”
Based on the incentive provided, there are two purchasing options:
Option 1:
One one-topping medium pizza for $7.99.
Option 2:
Two one-topping medium pizzas for $6.49 each.
To find the total price when two medium one-topping pizzas are purchased with the incentive, let's calculate the cost for each option:
Option 1:
The cost for one pizza is $7.99.
Option 2:
The cost for two pizzas at $6.49 each is:
2 * $6.49 = $12.98
Therefore, when two medium one-topping pizzas are purchased with the incentive, the total price would be $12.98 using Option 2.
Consider the following two monetary incentives when purchasing a desktop computer at the regular price of $299.
25% Off All Desktops with Regular Price of $200 or More.
$70 Rebate on Any Purchase of $200 or More.
Find the final price of the better incentive, after the discount has been applied. Round the answer to two decimal places.
Let's analyze both incentives and determine which one provides a better discount on the regular price of $299.
Incentive 1: 25% Off All Desktops with Regular Price of $200 or More.
25% of $299 is calculated as (25/100) * $299 = $74.75
However, the incentive specifies that it is applicable only to desktops with a regular price of $200 or more. Since $299 falls into this category, the discount is applicable.
Subtracting the discount from the regular price:
Final price = $299 - $74.75 = $224.25
Incentive 2: $70 Rebate on Any Purchase of $200 or More.
This incentive provides a straight $70 rebate on any purchase of $200 or more. Since the regular price of $299 falls into this category, the $70 rebate is applicable.
Subtracting the rebate from the regular price:
Final price = $299 - $70 = $229
Comparing the final prices, we find that the better incentive is the 25% off discount, which results in a final price of $224.25.
Kyle wants to purchase 20 prefilled decorated eggs to set up an egg hunt for his nephews and nieces. Each egg is priced at $5.00, and the store offers two different incentives.
Incentive 1: Purchase any set of 3 prefilled eggs for $12.
Incentive 2: Take 20% off your entire purchase.
Determine whether incentive 1 or incentive 2 offers a better discount. Find the discount amount. Round the answer to two decimal places as necessary.
Let's compare the two incentives to determine which one offers a better discount for purchasing 20 prefilled decorated eggs.
Incentive 1: Purchase any set of 3 prefilled eggs for $12.
Each set of 3 prefilled eggs costs $12.
To calculate the total cost for 20 eggs using this incentive:
Number of sets needed = 20 eggs / 3 eggs per set ≈ 6.67 (rounded up to 7 sets)
Total cost = 7 sets * $12 per set = $84
Incentive 2: Take 20% off your entire purchase.
The regular price for 20 eggs at $5.00 per egg is:
20 eggs * $5.00 per egg = $100
With a 20% discount, the discount amount is:
Discount amount = 20% * $100 = $20.00
Comparing the total cost under each incentive:
Incentive 1: $84
Incentive 2: $100 - $20 = $80
Therefore, Incentive 2 offers a better discount. The discount amount is $20.00.
Question
Use the table to answer the question.
Assets Value
Car $24,728
Savings account $3,589
Savings for retirement $15,600
Total Assets
Liabilities Balance Owed
Car loan $3,000
Credit card balance $762
Total Liabilities
Net Worth
Reena wants to put together a net worth statement to share with her bank as she applies for a small loan. Showing your work for each step, construct a net worth statement based on the information she has gathered in the table. What does this mean for Reena’s chances of getting a loan?
To construct a net worth statement based on the provided information, we need to calculate the total assets, total liabilities, and net worth:
Total Assets:
Car value: $24,728
Savings account: $3,589
Savings for retirement: $15,600
Total Assets = Car + Savings account + Savings for retirement
Total Assets = $24,728 + $3,589 + $15,600
Total Assets = $43,917
Total Liabilities:
Car loan balance owed: $3,000
Credit card balance owed: $762
Total Liabilities = Car loan + Credit card balance
Total Liabilities = $3,000 + $762
Total Liabilities = $3,762
Net Worth:
Net Worth = Total Assets - Total Liabilities
Net Worth = $43,917 - $3,762
Net Worth = $40,155
This means that Reena's net worth is $40,155.
Regarding Reena's chances of getting a loan, her positive net worth is generally a favorable factor. A higher net worth indicates that Reena has more assets than liabilities, which suggests she may have the financial capacity to repay the loan. However, the bank will consider other factors such as Reena's income, credit history, and the purpose of the loan before making a decision.
where did u get the 2 from
To find the difference between the two interest earning types (simple interest at 6.5% and compound interest at 6%), we need to calculate the interest earned by each option.
For Simple Interest:
Simple Interest = Principal * Rate * Time
Simple Interest = $6,700 * 0.065 * 3
Simple Interest = $1,302.50
For Compound Interest:
Compound Interest = Principal * (1 + Rate)^Time - Principal
Compound Interest = $6,700 * (1 + 0.06)^3 - $6,700
Compound Interest ≈ $1,215.74
The difference in interest earning is:
$1,302.50 - $1,215.74 = $86.76
Therefore, the difference between the two interest earning types is $86.76. Hence, Aria should invest with 6.5% simple interest because it will result in $86.76 more in interest earnings compared to compound interest at 6%.