Continuous Compound Interest Sample Problems

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These sample problems below for Continuous Compound Interest were generated by the MathScore.com engine.

Sample Problems For Continuous Compound Interest

Complexity=20, Mode=year

Answer the following questions involving continuously compounded interest. Input all answers to the nearest dollar. Use 2.7 as the value for e.

1.	Interest Rate: 3% per year Starting Balance: $1030 Time Passed: 9 years What is the new total balance? How much interest has accrued if calculated as continuously compounded interest?	Total balance: Interest:
2.	Interest Rate: 6% per year Starting Balance: $1380 Time Passed: 7 years What is the new total balance? How much interest has accrued if calculated as continuously compounded interest?	Total balance: Interest:

Complexity=50, Mode=year

Answer the following questions involving continuously compounded interest. Input all answers to the nearest dollar. Use 2.7 as the value for e.

1.	Interest Rate: 10% per year Starting Balance: $3060 Time Passed: 3 years What is the new total balance? How much interest has accrued if calculated as continuously compounded interest?	Total balance: Interest:
2.	Interest Rate: 2% per year Starting Balance: $4320 Time Passed: 12 years What is the new total balance? How much interest has accrued if calculated as continuously compounded interest?	Total balance: Interest:

Complexity=100, Mode=month

Answer the following questions involving continuously compounded interest. Input all answers to the nearest dollar. Use 2.7 as the value for e.

1.	Interest Rate: 7% per year Starting Balance: $6790 Time Passed: 60 months What is the new total balance? How much interest has accrued if calculated as continuously compounded interest?	Total balance: Interest:
2.	Interest Rate: 3% per year Starting Balance: $3600 Time Passed: 180 months What is the new total balance? How much interest has accrued if calculated as continuously compounded interest?	Total balance: Interest:

Answers

Complexity=20, Mode=year

Answer the following questions involving continuously compounded interest. Input all answers to the nearest dollar. Use 2.7 as the value for e.

#	Problem	Correct Answer	Your Answer
1	Interest Rate: 3% per year Starting Balance: $1030 Time Passed: 9 years What is the new total balance? How much interest has accrued if calculated as continuously compounded interest?	Total balance: Interest:
Solution Continuous compound interest: Total Balance = P × e^RT P = principle = starting balance = $1030 R = interest rate = 3% T = time = 9 years Total balance = principle × e^{(Rate × Time)} = 1030e^{(3 / 100) * 9} = 1030e^0.27= 1030 × (2.7^0.27) = $1347 Interest accrued = total balance - starting balance = $1347 - $1030 = $317

#	Problem	Correct Answer	Your Answer
2	Interest Rate: 6% per year Starting Balance: $1380 Time Passed: 7 years What is the new total balance? How much interest has accrued if calculated as continuously compounded interest?	Total balance: Interest:
Solution Continuous compound interest: Total Balance = P × e^RT P = principle = starting balance = $1380 R = interest rate = 6% T = time = 7 years Total balance = principle × e^{(Rate × Time)} = 1380e^{(6 / 100) * 7} = 1380e^0.42= 1380 × (2.7^0.42) = $2094 Interest accrued = total balance - starting balance = $2094 - $1380 = $714

Complexity=50, Mode=year

Answer the following questions involving continuously compounded interest. Input all answers to the nearest dollar. Use 2.7 as the value for e.

#	Problem	Correct Answer	Your Answer
1	Interest Rate: 10% per year Starting Balance: $3060 Time Passed: 3 years What is the new total balance? How much interest has accrued if calculated as continuously compounded interest?	Total balance: Interest:
Solution Continuous compound interest: Total Balance = P × e^RT P = principle = starting balance = $3060 R = interest rate = 10% T = time = 3 years Total balance = principle × e^{(Rate × Time)} = 3060e^{(10 / 100) * 3} = 3060e^0.3= 3060 × (2.7^0.3) = $4122 Interest accrued = total balance - starting balance = $4122 - $3060 = $1062

#	Problem	Correct Answer	Your Answer
2	Interest Rate: 2% per year Starting Balance: $4320 Time Passed: 12 years What is the new total balance? How much interest has accrued if calculated as continuously compounded interest?	Total balance: Interest:
Solution Continuous compound interest: Total Balance = P × e^RT P = principle = starting balance = $4320 R = interest rate = 2% T = time = 12 years Total balance = principle × e^{(Rate × Time)} = 4320e^{(2 / 100) * 12} = 4320e^0.24= 4320 × (2.7^0.24) = $5483 Interest accrued = total balance - starting balance = $5483 - $4320 = $1163

Complexity=100, Mode=month

Answer the following questions involving continuously compounded interest. Input all answers to the nearest dollar. Use 2.7 as the value for e.

#	Problem	Correct Answer	Your Answer
1	Interest Rate: 7% per year Starting Balance: $6790 Time Passed: 60 months What is the new total balance? How much interest has accrued if calculated as continuously compounded interest?	Total balance: Interest:
Solution Continuous compound interest: Total Balance = P × e^RT P = principle = starting balance = $6790 R = interest rate = 7% T = time = 60 months = 5 years Total balance = principle × e^{(Rate × Time)} = 6790e^{(7 / 100) * 5} = 6790e^0.35= 6790 × (2.7^0.35) = $9613 Interest accrued = total balance - starting balance = $9613 - $6790 = $2823

#	Problem	Correct Answer	Your Answer
2	Interest Rate: 3% per year Starting Balance: $3600 Time Passed: 180 months What is the new total balance? How much interest has accrued if calculated as continuously compounded interest?	Total balance: Interest:
Solution Continuous compound interest: Total Balance = P × e^RT P = principle = starting balance = $3600 R = interest rate = 3% T = time = 180 months = 15 years Total balance = principle × e^{(Rate × Time)} = 3600e^{(3 / 100) * 15} = 3600e^0.45= 3600 × (2.7^0.45) = $5629 Interest accrued = total balance - starting balance = $5629 - $3600 = $2029

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