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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: 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:
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:

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: $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:
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:

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: 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:
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:

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.

#ProblemCorrect AnswerYour Answer
1Interest 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 × eRT
P = principle = starting balance = $1090
R = interest rate = 6%
T = time = 7 years
Total balance = principle × e(Rate × Time) = 1090e(6 / 100) * 7 = 1090e0.42= 1090 × (2.70.42) = $1654
Interest accrued = total balance - starting balance = $1654 - $1090 = $564
#ProblemCorrect AnswerYour Answer
2Interest 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 × eRT
P = principle = starting balance = $1850
R = interest rate = 1%
T = time = 6 years
Total balance = principle × e(Rate × Time) = 1850e(1 / 100) * 6 = 1850e0.06= 1850 × (2.70.06) = $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.

#ProblemCorrect AnswerYour Answer
1Interest 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 × eRT
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
#ProblemCorrect AnswerYour Answer
2Interest 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 × eRT
P = principle = starting balance = $2370
R = interest rate = 6%
T = time = 15 years
Total balance = principle × e(Rate × Time) = 2370e(6 / 100) * 15 = 2370e0.9= 2370 × (2.70.9) = $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.

#ProblemCorrect AnswerYour Answer
1Interest 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 × eRT
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 = 9880e0.39= 9880 × (2.70.39) = $14554
Interest accrued = total balance - starting balance = $14554 - $9880 = $4674
#ProblemCorrect AnswerYour Answer
2Interest 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 × eRT
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 = 9890e0.45= 9890 × (2.70.45) = $15464
Interest accrued = total balance - starting balance = $15464 - $9890 = $5574
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