Math Practice Problems - Continuous Compound Interest

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Continuous Compound Interest - Sample Math Practice Problems

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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.

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.

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: 6% per year Starting Balance: $1090 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 = $1090 R = interest rate = 6% T = time = 7 years Total balance = principle × e^{(Rate × Time)} = 1090e^{(6 / 100) * 7} = 1090e^0.42= 1090 × (2.7^0.42) = $1654 Interest accrued = total balance - starting balance = $1654 - $1090 = $564

#	Problem	Correct Answer	Your Answer
2	Interest Rate: 1% per year Starting Balance: $1850 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 = $1850 R = interest rate = 1% T = time = 6 years Total balance = principle × e^{(Rate × Time)} = 1850e^{(1 / 100) * 6} = 1850e^0.06= 1850 × (2.7^0.06) = $1964 Interest accrued = total balance - starting balance = $1964 - $1850 = $114

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: $3050 Time Passed: 10 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 = $3050 R = interest rate = 10% T = time = 10 years Total balance = principle × e^{(Rate × Time)} = 3050e^{(10 / 100) * 10} = 3050e¹= 3050 × (2.7¹) = $8235 Interest accrued = total balance - starting balance = $8235 - $3050 = $5185

#	Problem	Correct Answer	Your Answer
2	Interest Rate: 6% per year Starting Balance: $2370 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 = $2370 R = interest rate = 6% T = time = 15 years Total balance = principle × e^{(Rate × Time)} = 2370e^{(6 / 100) * 15} = 2370e^0.9= 2370 × (2.7^0.9) = $5794 Interest accrued = total balance - starting balance = $5794 - $2370 = $3424

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: 3% per year Starting Balance: $9880 Time Passed: 156 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 = $9880 R = interest rate = 3% T = time = 156 months = 13 years Total balance = principle × e^{(Rate × Time)} = 9880e^{(3 / 100) * 13} = 9880e^0.39= 9880 × (2.7^0.39) = $14554 Interest accrued = total balance - starting balance = $14554 - $9880 = $4674

#	Problem	Correct Answer	Your Answer
2	Interest Rate: 9% per year Starting Balance: $9890 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 = $9890 R = interest rate = 9% T = time = 60 months = 5 years Total balance = principle × e^{(Rate × Time)} = 9890e^{(9 / 100) * 5} = 9890e^0.45= 9890 × (2.7^0.45) = $15464 Interest accrued = total balance - starting balance = $15464 - $9890 = $5574

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