Calculate the simple interest on a $20,000 loan at an interest rate of 8 percent after 5 years.(1 point)
Responses
$8,000
$8,000
$800,000
$800,000
$80,000
$80,000
$1,600
The simple interest on a $20,000 loan at an interest rate of 8 percent after 5 years can be calculated using the formula:
Simple Interest = Principle × Rate × Time
In this case, the principle is $20,000, the rate is 0.08 (8 percent written as a decimal), and the time is 5 years.
Using the formula:
Simple Interest = $20,000 × 0.08 × 5 = $8,000
Therefore, the simple interest on a $20,000 loan at an interest rate of 8 percent after 5 years is $8,000.
Calculate the amount to be paid back after three years on a $3,000 credit card loan with an interest rate of 15% compounded yearly. (1 point)
Responses
$4,562.63
$4,562.63
$267,572.61
$267,572.61
$4,271.48
$4,271.48
$3,138.08
To calculate the amount to be paid back after three years on a $3,000 credit card loan with an interest rate of 15% compounded yearly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount to be paid back
P = the principal amount (initial loan amount)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, P = $3,000, r = 0.15, n = 1 (compounded yearly), and t = 3.
A = $3,000(1 + 0.15/1)^(1*3)
A = $3,000(1 + 0.15)^3
A = $3,000(1.15)^3
A = $3,000 * 1.520875
A = $4,562.63
Therefore, the amount to be paid back after three years on a $3,000 credit card loan with an interest rate of 15% compounded yearly is $4,562.63.
Calculate the amount to be paid back on a $20,000 loan with an interest rate of 12% compounded yearly after five years.(1 point)
Responses
$35,246.83
$35,246.83
$640,000
$640,000
$1,030,726
$1,030,726
$51,470
To calculate the amount to be paid back on a $20,000 loan with an interest rate of 12% compounded yearly after five years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount to be paid back
P = the principal amount (initial loan amount)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, P = $20,000, r = 0.12, n = 1 (compounded yearly), and t = 5.
A = $20,000(1 + 0.12/1)^(1*5)
A = $20,000(1 + 0.12)^5
A = $20,000(1.12)^5
A = $20,000 * 1.7623413
A = $35,246.83
Therefore, the amount to be paid back on a $20,000 loan with an interest rate of 12% compounded yearly after five years is $35,246.83.
Compare simple interest at 7.5% and compound interest at 7.0% when $4,300 is invested for 2 years to determine which interest earning type will result in a higher balance. Find this balance.(1 point)
Responses
Simple interest at 7.5% results in a higher balance of $645 after 2 years of investment.
Simple interest at 7.5% results in a higher balance of $645 after 2 years of investment.
Simple interest at 7.5% results in a higher balance of $4,923.07 after 2 years of investment.
Simple interest at 7.5% results in a higher balance of $4,923.07 after 2 years of investment.
Simple interest at 7.5% results in a higher balance of $4,945 after 2 years of investment.
Simple interest at 7.5% results in a higher balance of $4,945 after 2 years of investment.
Compound interest at 7% results in a higher balance of $4,945 after 2 years of investment.
To compare the simple interest at 7.5% and the compound interest at 7.0% when $4,300 is invested for 2 years, we can calculate the balance for each type of interest individually.
For simple interest:
Interest = Principal * Rate * Time
Interest = $4,300 * 0.075 * 2
Interest = $645
The balance after 2 years of investment with simple interest would be $4,300 + $645 = $4,945.
For compound interest:
A = P * (1 + r/n)^(n*t)
A = $4,300 * (1 + 0.07/1)^(1*2)
A = $4,300 * (1.07)^2
A = $4,300 * 1.1449
A = $4,923.07
The balance after 2 years of investment with compound interest would be $4,923.07.
Therefore, the correct response is:
Compound interest at 7% results in a higher balance of $4,945 after 2 years of investment.
Find the difference in the balance between simple interest at 5% and compound interest at 6% when $900 is invested for a period of 5 years.(1 point)
Responses
$304.40
$304.40
$1,204.40
$1,204.40
$79.40
$79.40
$225
To find the difference in the balance between simple interest at 5% and compound interest at 6% when $900 is invested for a period of 5 years, we need to calculate the balance for each type of interest and then find the difference between them.
For simple interest:
Interest = Principal * Rate * Time
Interest = $900 * 0.05 * 5
Interest = $225
The balance after 5 years of investment with simple interest would be $900 + $225 = $1,125.
For compound interest:
A = P * (1 + r/n)^(n*t)
A = $900 * (1 + 0.06/1)^(1*5)
A = $900 * (1.06)^5
A = $900 * 1.338225
A = $1,204.40
The balance after 5 years of investment with compound interest would be $1,204.40.
Therefore, the difference in the balance between simple interest at 5% and compound interest at 6% is:
$1,204.40 - $1,125 = $79.40.
Therefore, the correct response is:
$79.40.