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 $….. and the final amount of the investment is $……
The accrued interest can be calculated using the formula: accrued interest = principal * rate * time.
For this problem, the principal is $10,000, the interest rate is 4.75%, and the time is 13 years.
Accrued interest = $10,000 * 0.0475 * 13 = $6,175.00
The final amount of the investment can be calculated by adding the accrued interest to the principal.
Final amount = $10,000 + $6,175.00 = $16,175.00
Therefore, the accrued interest is $6,175.00 and the final amount of the investment is $16,175.00.
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 $
To calculate the final amount of the investment after 27 years with quarterly compounding, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount of the investment
P = principal amount (initial investment) = $15,000
r = annual interest rate (as a decimal) = 3.4% = 0.034
n = number of times interest is compounded per year = 4 (quarterly compounding)
t = number of years
Plugging in the values:
A = $15,000(1 + 0.034/4)^(4*27)
Calculating inside the brackets:
(1 + 0.034/4)^(4*27) = (1.0085)^108
Calculating the final amount:
A = $15,000 * (1.0085)^108
A ≈ $15,000 * 3.171386646307036
A ≈ $47,570.80
Therefore, the final amount of the investment after 27 years with quarterly compounding is $47,570.80.
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 $, and the amount of interest gained is $
To calculate the final amount of the college fund after 18 years with monthly compounding interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount of the college fund
P = principal amount (initial investment) = $5,000
r = annual interest rate (as a decimal) = 7.3% = 0.073
n = number of times interest is compounded per year = 12 (monthly compounding)
t = number of years
Plugging in the values:
A = $5,000(1 + 0.073/12)^(12*18)
Calculating inside the brackets:
(1 + 0.073/12)^(12*18) = (1.00608333)^216
Calculating the final amount:
A = $5,000 * (1.00608333)^216
A ≈ $5,000 * 3.0594865378727827
A ≈ $15,297.43 (rounded to two decimal places)
To calculate the amount of interest gained, we subtract the principal amount from the final amount:
Interest = Final amount - Principal amount
Interest = $15,297.43 - $5,000
Interest ≈ $10,297.43 (rounded to two decimal places)
Therefore, the final amount of the college fund after 18 years with monthly compounding is approximately $15,297.43, and the amount of interest gained is approximately $10,297.43.
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.
To find the difference in interest earnings, we need to calculate the interest earned for each option and then subtract the interest earned for option 1 from the interest earned for option 2.
For Option 1, using the formula for simple interest:
Interest = Principal * Rate * Time
Interest = $7,000 * 0.15 * 3
Interest = $3,150
For Option 2, using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount of the investment
P = principal amount (initial investment) = $7,000
r = annual interest rate (as a decimal) = 12% = 0.12
n = number of times interest is compounded per year = 4 (quarterly compounding)
t = number of years = 3
A = $7,000 * (1 + 0.12/4)^(4*3)
A = $7,000 * (1.03)^12
A ≈ $9,257.56
Interest earned for Option 2 is the final amount minus the principal:
Interest = A - P
Interest = $9,257.56 - $7,000
Interest ≈ $2,257.56
The difference in interest earnings is the interest earned for Option 2 minus the interest earned for Option 1:
Difference = Interest (Option 2) - Interest (Option 1)
Difference = $2,257.56 - $3,150
Difference ≈ -$892.44
Therefore, the difference in interest earnings is approximately -$892.44. Since the difference is negative, it means that Option 1 (15% simple interest rate) will give greater financial returns.
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 offers the lower cost of credit, which is $
To determine which plan offers the student a lower cost of credit, we need to calculate the total amount repaid for each plan and compare them.
For Plan 1, we can calculate the total amount repaid by multiplying the monthly payment by the number of months:
Total amount repaid for Plan 1 = Monthly payment for Plan 1 * Number of months
Total amount repaid for Plan 1 = $361.91 * (10 years * 12 months/year)
Total amount repaid for Plan 1 = $361.91 * 120
Total amount repaid for Plan 1 = $43,429.20
For Plan 2, we can calculate the total amount repaid by multiplying the monthly payment by the number of months:
Total amount repaid for Plan 2 = Monthly payment for Plan 2 * Number of months
Total amount repaid for Plan 2 = $473.49 * (7 years * 12 months/year)
Total amount repaid for Plan 2 = $473.49 * 84
Total amount repaid for Plan 2 = $39,839.16
To find the lower cost of credit, we need to subtract the original loan amount from the total amount repaid for each plan:
Cost of credit for Plan 1 = Total amount repaid for Plan 1 - Loan amount
Cost of credit for Plan 1 = $43,429.20 - $33,500
Cost of credit for Plan 1 = $9,929.20
Cost of credit for Plan 2 = Total amount repaid for Plan 2 - Loan amount
Cost of credit for Plan 2 = $39,839.16 - $33,500
Cost of credit for Plan 2 = $6,339.16
The lower cost of credit is $6,339.16, which is offered by Plan 2.
Therefore, Plan 2 offers the student a lower cost of credit, which is $6,339.16.
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 $ the fixed monthly payment amount is $ The total amount of interest paid is $