The formula for calculating simple interest is:
Accrued Interest = Principal * Rate * Time
Given:
Principal = $10,000
Rate = 4.75% = 0.0475 (as a decimal)
Time = 13 years
Accrued Interest = $10,000 * 0.0475 * 13 = $6,175
The final amount of the investment can be calculated by adding the accrued interest to the principal:
Final Amount = Principal + Accrued Interest = $10,000 + $6,175 = $16,175
Therefore, the accrued interest is $6,175 and the final amount of the investment is $16,175.
Determine the accrued interest and the final amount of a $10,000 investment with a 4.75% simple interest rate over a period of 13 years. Round the answers to two decimal places as needed. (1 point)
The accrued interest is $ blank
and the final amount of the investment is
$ blank
11 answers
Chris invests $15,000 in a retirement account with an annual interest rate of 3.4%. Find the final amount of the investment after 27 years if interest is compounded quarterly.
Round the answer to the nearest cent. (1 point)
The final amount of the investment after 27 years is $
Round the answer to the nearest cent. (1 point)
The final amount of the investment after 27 years is $
To calculate the final amount of the investment after 27 years with quarterly compounding, we can use the formula for compound interest:
Final Amount = Principal * (1 + Rate/Number of Compounding Periods)^(Number of Compounding Periods * Time)
Given:
Principal = $15,000
Rate = 3.4% = 0.034 (as a decimal)
Number of Compounding Periods = 4 (quarterly compounding)
Time = 27 years
Final Amount = $15,000 * (1 + 0.034/4)^(4 * 27)
Final Amount = $15,000 * (1 + 0.0085)^108
Final Amount = $15,000 * (1.0085)^108
Final Amount ≈ $47,876.26
Therefore, the final amount of the investment after 27 years with quarterly compounding is approximately $47,876.26.
Final Amount = Principal * (1 + Rate/Number of Compounding Periods)^(Number of Compounding Periods * Time)
Given:
Principal = $15,000
Rate = 3.4% = 0.034 (as a decimal)
Number of Compounding Periods = 4 (quarterly compounding)
Time = 27 years
Final Amount = $15,000 * (1 + 0.034/4)^(4 * 27)
Final Amount = $15,000 * (1 + 0.0085)^108
Final Amount = $15,000 * (1.0085)^108
Final Amount ≈ $47,876.26
Therefore, the final amount of the investment after 27 years with quarterly compounding is approximately $47,876.26.
When Martin was born, his father set up a $5,000 college fund for him with an annual compound interest rate of 7.3%. What is the final amount of this college fund, and how much interest is gained if this fund is invested for 18 years if interest is compounded monthly? Round the answers to two decimal places as needed. (1 point)
The final amount of the college fund is $ blank
, and the amount of interest gained is $ blank
The final amount of the college fund is $ blank
, and the amount of interest gained is $ blank
To calculate the final amount of the college fund after 18 years with monthly compounding, we can use the formula for compound interest:
Final Amount = Principal * (1 + Rate/Number of Compounding Periods)^(Number of Compounding Periods * Time)
Given:
Principal = $5,000
Rate = 7.3% = 0.073 (as a decimal)
Number of Compounding Periods = 12 (monthly compounding)
Time = 18 years
Final Amount = $5,000 * (1 + 0.073/12)^(12 * 18)
Final Amount = $5,000 * (1 + 0.00608333)^216
Final Amount = $5,000 * (1.00608333)^216
Final Amount ≈ $16,372.51
To calculate the amount of interest gained, we can subtract the principal amount from the final amount:
Amount of Interest Gained = Final Amount - Principal = $16,372.51 - $5,000 = $11,372.51
Therefore, the final amount of the college fund after 18 years with monthly compounding is approximately $16,372.51, and the amount of interest gained is approximately $11,372.51.
Final Amount = Principal * (1 + Rate/Number of Compounding Periods)^(Number of Compounding Periods * Time)
Given:
Principal = $5,000
Rate = 7.3% = 0.073 (as a decimal)
Number of Compounding Periods = 12 (monthly compounding)
Time = 18 years
Final Amount = $5,000 * (1 + 0.073/12)^(12 * 18)
Final Amount = $5,000 * (1 + 0.00608333)^216
Final Amount = $5,000 * (1.00608333)^216
Final Amount ≈ $16,372.51
To calculate the amount of interest gained, we can subtract the principal amount from the final amount:
Amount of Interest Gained = Final Amount - Principal = $16,372.51 - $5,000 = $11,372.51
Therefore, the final amount of the college fund after 18 years with monthly compounding is approximately $16,372.51, and the amount of interest gained is approximately $11,372.51.
Angel wants to invest $7,000 for 3 years. He has two investing options.
• Option 1: Investing with a 15% simple interest rate.
• Option 2: Investing with a 12% compound interest rate, with interest being compounded quarterly.
Find the difference in interest earnings to help Angel determine which investing option will give more financial returns.
(1 point)
The difference in interest earnings is $
and option
is the better investing option.
• Option 1: Investing with a 15% simple interest rate.
• Option 2: Investing with a 12% compound interest rate, with interest being compounded quarterly.
Find the difference in interest earnings to help Angel determine which investing option will give more financial returns.
(1 point)
The difference in interest earnings is $
and option
is the better investing option.
To find the difference in interest earnings between the two investing options, we need to calculate the interest earned in each option and then subtract them.
Option 1:
Principal = $7,000
Rate = 15% = 0.15 (as a decimal)
Time = 3 years
Interest Earned (Option 1) = Principal * Rate * Time
Interest Earned (Option 1) = $7,000 * 0.15 * 3
Interest Earned (Option 1) = $3,150
Option 2:
Principal = $7,000
Rate = 12% = 0.12 (as a decimal)
Number of Compounding Periods = 4 (quarterly compounding)
Time = 3 years
Final Amount (Option 2) = Principal * (1 + Rate/Number of Compounding Periods)^(Number of Compounding Periods * Time)
Final Amount (Option 2) = $7,000 * (1 + 0.12/4)^(4 * 3)
Final Amount (Option 2) = $7,000 * (1 + 0.03)^12
Final Amount (Option 2) ≈ $9,022.28
Interest Earned (Option 2) = Final Amount (Option 2) - Principal
Interest Earned (Option 2) ≈ $9,022.28 - $7,000
Interest Earned (Option 2) ≈ $2,022.28
Difference in Interest Earnings = Interest Earned (Option 2) - Interest Earned (Option 1)
Difference in Interest Earnings = $2,022.28 - $3,150
Difference in Interest Earnings ≈ -$1,127.72
Therefore, the difference in interest earnings is approximately -$1,127.72. This means that Option 1 (investing with a 15% simple interest rate) yields higher returns than Option 2 (investing with a 12% compound interest rate, compounded quarterly).
Option 1:
Principal = $7,000
Rate = 15% = 0.15 (as a decimal)
Time = 3 years
Interest Earned (Option 1) = Principal * Rate * Time
Interest Earned (Option 1) = $7,000 * 0.15 * 3
Interest Earned (Option 1) = $3,150
Option 2:
Principal = $7,000
Rate = 12% = 0.12 (as a decimal)
Number of Compounding Periods = 4 (quarterly compounding)
Time = 3 years
Final Amount (Option 2) = Principal * (1 + Rate/Number of Compounding Periods)^(Number of Compounding Periods * Time)
Final Amount (Option 2) = $7,000 * (1 + 0.12/4)^(4 * 3)
Final Amount (Option 2) = $7,000 * (1 + 0.03)^12
Final Amount (Option 2) ≈ $9,022.28
Interest Earned (Option 2) = Final Amount (Option 2) - Principal
Interest Earned (Option 2) ≈ $9,022.28 - $7,000
Interest Earned (Option 2) ≈ $2,022.28
Difference in Interest Earnings = Interest Earned (Option 2) - Interest Earned (Option 1)
Difference in Interest Earnings = $2,022.28 - $3,150
Difference in Interest Earnings ≈ -$1,127.72
Therefore, the difference in interest earnings is approximately -$1,127.72. This means that Option 1 (investing with a 15% simple interest rate) yields higher returns than Option 2 (investing with a 12% compound interest rate, compounded quarterly).
A student with a $33,500 student loan is offered two payment plans to repay their debt.
• Plan 1: Monthly payment of $361.91 over a period of 10 years, which corresponds to a compound interest rate of 5.4% compounded monthly.
• Plan 2: Monthly payment of $473.49 over a period of 7 years, which corresponds to a compound interest rate of 5.0% compounded monthly.
Determine which plan offers the student a lower cost of credit. Find the lower credit cost. Round the answer to two decimal places as needed.
(1 point)
Plan blank
offers the lower cost of credit, which is $ blank
• Plan 1: Monthly payment of $361.91 over a period of 10 years, which corresponds to a compound interest rate of 5.4% compounded monthly.
• Plan 2: Monthly payment of $473.49 over a period of 7 years, which corresponds to a compound interest rate of 5.0% compounded monthly.
Determine which plan offers the student a lower cost of credit. Find the lower credit cost. Round the answer to two decimal places as needed.
(1 point)
Plan blank
offers the lower cost of credit, which is $ blank
To determine which plan offers the student a lower cost of credit, we need to calculate the total amount paid for each plan and then compare them.
Plan 1:
Monthly Payment = $361.91
Number of Payments = 10 years * 12 months = 120 months
Rate = 5.4% = 0.054 (as a decimal)
Total Amount Paid (Plan 1) = Monthly Payment * Number of Payments = $361.91 * 120 = $43,429.20
Plan 2:
Monthly Payment = $473.49
Number of Payments = 7 years * 12 months = 84 months
Rate = 5.0% = 0.05 (as a decimal)
Total Amount Paid (Plan 2) = Monthly Payment * Number of Payments = $473.49 * 84 = $39,850.16
Therefore, Plan 2 offers the student a lower cost of credit. The lower cost of credit is approximately $39,850.16.
Plan 1:
Monthly Payment = $361.91
Number of Payments = 10 years * 12 months = 120 months
Rate = 5.4% = 0.054 (as a decimal)
Total Amount Paid (Plan 1) = Monthly Payment * Number of Payments = $361.91 * 120 = $43,429.20
Plan 2:
Monthly Payment = $473.49
Number of Payments = 7 years * 12 months = 84 months
Rate = 5.0% = 0.05 (as a decimal)
Total Amount Paid (Plan 2) = Monthly Payment * Number of Payments = $473.49 * 84 = $39,850.16
Therefore, Plan 2 offers the student a lower cost of credit. The lower cost of credit is approximately $39,850.16.
Using an online calculator, determine the total cost, fixed monthly payment, and the total interest paid when repaying a credit card loan of $3,500 with a 21% interest rate compounded monthly over a 24-month term. Round the answer to the nearest dollar. (2 points)
To the nearest dollar, the total cost of repaying the loan is $ Blank The fixed monthly payment amount is $ blank
The total amount of interest paid is $ blank
To the nearest dollar, the total cost of repaying the loan is $ Blank The fixed monthly payment amount is $ blank
The total amount of interest paid is $ blank
To determine the total cost, fixed monthly payment, and total interest paid when repaying a credit card loan of $3,500 with a 21% interest rate compounded monthly over a 24-month term, we can use an online loan calculator or the following formulas:
Monthly Payment = (Principal * Rate) / (1 - (1 + Rate)^(-Time))
Total Cost = Monthly Payment * Time
Total Interest Paid = Total Cost - Principal
Given:
Principal = $3,500
Rate = 21% = 0.21 (as a decimal)
Time = 24 months
Using the formulas:
Monthly Payment = ($3,500 * 0.21) / (1 - (1 + 0.21)^(-24))
Monthly Payment ≈ $188
Total Cost = $188 * 24
Total Cost = $4,512
Total Interest Paid = $4,512 - $3,500
Total Interest Paid ≈ $1,012
Therefore, the total cost of repaying the loan is approximately $4,512, the fixed monthly payment amount is approximately $188, and the total amount of interest paid is approximately $1,012.
Monthly Payment = (Principal * Rate) / (1 - (1 + Rate)^(-Time))
Total Cost = Monthly Payment * Time
Total Interest Paid = Total Cost - Principal
Given:
Principal = $3,500
Rate = 21% = 0.21 (as a decimal)
Time = 24 months
Using the formulas:
Monthly Payment = ($3,500 * 0.21) / (1 - (1 + 0.21)^(-24))
Monthly Payment ≈ $188
Total Cost = $188 * 24
Total Cost = $4,512
Total Interest Paid = $4,512 - $3,500
Total Interest Paid ≈ $1,012
Therefore, the total cost of repaying the loan is approximately $4,512, the fixed monthly payment amount is approximately $188, and the total amount of interest paid is approximately $1,012.
11 answers