Math Practice Problems - Continuous Compound Interest

Continuous Compound Interest - Sample Math Practice Problems

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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: 5% per year Starting Balance: $1200 Time Passed: 6 years What is the new total balance? How much interest has accrued if calculated as continuously compounded interest?	Total balance: Interest:
2.	Interest Rate: 9% per year Starting Balance: $1120 Time Passed: 11 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: 4% per year Starting Balance: $3020 Time Passed: 15 years What is the new total balance? How much interest has accrued if calculated as continuously compounded interest?	Total balance: Interest:
2.	Interest Rate: 4% per year Starting Balance: $1800 Time Passed: 8 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: 10% per year Starting Balance: $1210 Time Passed: 144 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: $9020 Time Passed: 12 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: 5% per year Starting Balance: $1200 Time Passed: 6 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 = $1200 R = interest rate = 5% T = time = 6 years Total balance = principle × e^{(Rate × Time)} = 1200e^{(5 / 100) * 6} = 1200e^0.3= 1200 × (2.7^0.3) = $1617 Interest accrued = total balance - starting balance = $1617 - $1200 = $417

#	Problem	Correct Answer	Your Answer
2	Interest Rate: 9% per year Starting Balance: $1120 Time Passed: 11 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 = $1120 R = interest rate = 9% T = time = 11 years Total balance = principle × e^{(Rate × Time)} = 1120e^{(9 / 100) * 11} = 1120e^0.99= 1120 × (2.7^0.99) = $2994 Interest accrued = total balance - starting balance = $2994 - $1120 = $1874

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: 4% per year Starting Balance: $3020 Time Passed: 15 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 = $3020 R = interest rate = 4% T = time = 15 years Total balance = principle × e^{(Rate × Time)} = 3020e^{(4 / 100) * 15} = 3020e^0.6= 3020 × (2.7^0.6) = $5481 Interest accrued = total balance - starting balance = $5481 - $3020 = $2461

#	Problem	Correct Answer	Your Answer
2	Interest Rate: 4% per year Starting Balance: $1800 Time Passed: 8 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 = $1800 R = interest rate = 4% T = time = 8 years Total balance = principle × e^{(Rate × Time)} = 1800e^{(4 / 100) * 8} = 1800e^0.32= 1800 × (2.7^0.32) = $2473 Interest accrued = total balance - starting balance = $2473 - $1800 = $673

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: 10% per year Starting Balance: $1210 Time Passed: 144 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 = $1210 R = interest rate = 10% T = time = 144 months = 12 years Total balance = principle × e^{(Rate × Time)} = 1210e^{(10 / 100) * 12} = 1210e^1.2= 1210 × (2.7^1.2) = $3985 Interest accrued = total balance - starting balance = $3985 - $1210 = $2775

#	Problem	Correct Answer	Your Answer
2	Interest Rate: 3% per year Starting Balance: $9020 Time Passed: 12 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 = $9020 R = interest rate = 3% T = time = 12 months = 1 year Total balance = principle × e^{(Rate × Time)} = 9020e^{(3 / 100) * 1} = 9020e^0.03= 9020 × (2.7^0.03) = $9293 Interest accrued = total balance - starting balance = $9293 - $9020 = $273

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