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
$51,470
$51,470
$1,030,726
$1,030,726
$640,000
$640,000
$35,246.83
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 compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount to be paid back
P = the principal amount (initial loan amount)
r = annual interest rate (as a decimal)
n = number of times compounded per year
t = number of years
Given:
P = $20,000
r = 12% = 0.12 (as a decimal)
n = 1 (compounded yearly)
t = 5 years
Plugging the values into the formula:
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(1.7623)
A ≈ $35,246.83
Therefore, the correct amount to be paid back on this loan after five years would be approximately $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
Compound interest at 7% 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.
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 $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 $4,945 after 2 years of investment.
To determine which interest earning type will result in a higher balance, we can calculate the balances using both simple interest and compound interest formulas.
Given:
Principal (P) = $4,300
Time (t) = 2 years
For simple interest:
Interest rate (r) = 7.5% = 0.075 (as a decimal)
Simple interest formula:
A = P(1 + rt)
For compound interest:
Interest rate (r) = 7.0% = 0.07 (as a decimal)
Number of compounding periods (n) = 1 (compounded yearly)
Compound interest formula:
A = P(1 + r/n)^(nt)
Calculating the simple interest balance:
A_simple = $4,300(1 + 0.075*2)
A_simple = $4,300(1 + 0.15)
A_simple = $4,300(1.15)
A_simple ≈ $4,945
Calculating the compound interest balance:
A_compound = $4,300(1 + 0.07/1)^(1*2)
A_compound = $4,300(1 + 0.07)^2
A_compound = $4,300(1.07)^2
A_compound = $4,300(1.1449)
A_compound ≈ $4,924.07
Therefore, the correct option is:
Compound interest at 7% results in a higher balance of $4,924.07 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
$225
$225
$304.40
$304.40
$79.40
$79.40
$1,204.40
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 can calculate the balances using the simple interest and compound interest formulas.
Given:
Principal (P) = $900
Time (t) = 5 years
For simple interest:
Interest rate (r) = 5% = 0.05 (as a decimal)
Simple interest formula:
A_simple = P(1 + rt)
For compound interest:
Interest rate (r) = 6% = 0.06 (as a decimal)
Number of compounding periods (n) = 1 (compounded yearly)
Compound interest formula:
A_compound = P(1 + r/n)^(nt)
Calculating the balance with simple interest:
A_simple = $900(1 + 0.05*5)
A_simple = $900(1 + 0.25)
A_simple = $900(1.25)
A_simple = $1,125
Calculating the balance with compound interest:
A_compound = $900(1 + 0.06/1)^(1*5)
A_compound = $900(1 + 0.06)^5
A_compound = $900(1.06)^5
A_compound ≈ $1,129.40
Difference in balance = A_compound - A_simple
Difference in balance = $1,129.40 - $1,125
Difference in balance ≈ $4.40
Therefore, the correct answer is:
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 is approximately $4.40.