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## Continuous Compound Interest - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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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: \$1090Time 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: \$1850Time 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: \$3050Time 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: \$2370Time 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: \$9880Time 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: \$9890Time Passed: 60 months What is the new total balance? How much interest has accrued if calculated as continuously compounded interest?   Total balance:   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.

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
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.

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
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.

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
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