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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: \$1030Time 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: \$1380Time 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: \$3060Time 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: \$4320Time 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: \$6790Time 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: \$3600Time Passed: 180 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: 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 × eRT
P = principle = starting balance = \$1030
R = interest rate = 3%
T = time = 9 years
Total balance = principle × e(Rate × Time) = 1030e(3 / 100) * 9 = 1030e0.27= 1030 × (2.70.27) = \$1347
Interest accrued = total balance - starting balance = \$1347 - \$1030 = \$317
2Interest 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 × eRT
P = principle = starting balance = \$1380
R = interest rate = 6%
T = time = 7 years
Total balance = principle × e(Rate × Time) = 1380e(6 / 100) * 7 = 1380e0.42= 1380 × (2.70.42) = \$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.
1Interest 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 × eRT
P = principle = starting balance = \$3060
R = interest rate = 10%
T = time = 3 years
Total balance = principle × e(Rate × Time) = 3060e(10 / 100) * 3 = 3060e0.3= 3060 × (2.70.3) = \$4122
Interest accrued = total balance - starting balance = \$4122 - \$3060 = \$1062
2Interest 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 × eRT
P = principle = starting balance = \$4320
R = interest rate = 2%
T = time = 12 years
Total balance = principle × e(Rate × Time) = 4320e(2 / 100) * 12 = 4320e0.24= 4320 × (2.70.24) = \$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.
1Interest 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 × eRT
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 = 6790e0.35= 6790 × (2.70.35) = \$9613
Interest accrued = total balance - starting balance = \$9613 - \$6790 = \$2823
2Interest 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 × eRT
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 = 3600e0.45= 3600 × (2.70.45) = \$5629
Interest accrued = total balance - starting balance = \$5629 - \$3600 = \$2029

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