Question

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)

Answer 1

[AI-generated answer — Bot GPT 3.5]

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 future value of the loan (the amount to be paid back)
P = the principal amount (the 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 = 15% = 0.15, n = 1 (compounded yearly), and t = 3 years.

A = 3000(1 + 0.15/1)^(1*3)
A = 3000(1 + 0.15)^3
A = 3000(1.15)^3
A = 3000 * 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.

Answer 2

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)

Answer 3

[AI-generated answer — Bot GPT 3.5]

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 future value of the loan (the amount to be paid back)
P = the principal amount (the 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 = 12% = 0.12, n = 1 (compounded yearly), and t = 5 years.

A = 20000(1 + 0.12/1)^(1*5)
A = 20000(1 + 0.12)^5
A = 20000(1.12)^5
A = 20000 * 1.762341
A = $35,246.82

Therefore, the amount to be paid back on a $20,000 loan with an interest rate of 12% compounded yearly after five years is $35,246.82.

Answer 4

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)

Answer 5

[AI-generated answer — Bot GPT 3.5]

To compare simple interest at 7.5% and compound interest at 7.0% when $4,300 is invested for 2 years, we will calculate the balance for each type of interest.

For simple interest, the formula is:
A = P(1 + rt)
Where:
A = the future value (balance)
P = the principal amount (initial investment)
r = the interest rate (as a decimal)
t = the number of years

For compound interest, the formula is:
A = P(1 + r/n)^(nt)
Where:
A = the future value (balance)
P = the principal amount (initial investment)
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 = $4,300, r1 = 7.5% = 0.075, r2 = 7.0% = 0.07, t = 2 years, and n = 1 (compounded annually).

Simple Interest:
A1 = 4300(1 + 0.075 * 2)
A1 = 4300(1.15)
A1 = $4945

Compound Interest:
A2 = 4300(1 + 0.07/1)^(1 * 2)
A2 = 4300(1 + 0.07)^2
A2 = 4300(1.07)^2
A2 = 4300 * 1.1449
A2 = $4929.07

Therefore, the balance after 2 years with simple interest at 7.5% is $4,945, while the balance with compound interest at 7.0% is $4,929.07. Simple interest yields a higher balance in this case.

Answer 6

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

$225
$225

$79.40
$79.40

$1,204.40
$1,204.40

$304.40

Answer 7

[AI-generated answer — Bot GPT 3.5]

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 will calculate the balances for each type of interest separately.

For simple interest, the formula is:
A = P(1 + rt)
Where:
A = the future value (balance)
P = the principal amount (initial investment)
r = the interest rate (as a decimal)
t = the number of years

For compound interest, the formula is:
A = P(1 + r/n)^(nt)
Where:
A = the future value (balance)
P = the principal amount (initial investment)
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 = $900, r1 = 5% = 0.05, r2 = 6% = 0.06, t = 5 years, and n = 1 (compounded annually).

Simple Interest:
A1 = 900(1 + 0.05 * 5)
A1 = 900(1.25)
A1 = $1125

Compound Interest:
A2 = 900(1 + 0.06/1)^(1 * 5)
A2 = 900(1 + 0.06)^5
A2 = 900(1.06)^5
A2 = 900 * 1.3382
A2 = $1204.38 (rounded to the nearest hundredth)

The difference in the balance between simple interest at 5% and compound interest at 6% is:

1204.38 - 1125 = $79.38

Therefore, the correct response is:
$79.40