DIFFERENTIAL EQUATION INSTRUCTIONAL MATERIALS
PROBLEM SETS
TOPIC: CONTINUOUS COMPOUND INTEREST
CONTINUOUS COMPOUND INTEREST
PROBLEM SET
General Formula: 𝑷 = 𝒄𝒆𝒓𝒕
EASY
1. Suho opened a savings account and deposited 800.00 Pesos as principal. The
account earns 15% interest, compounded continuously. What is the balance
after 3 years?
When 𝐶 = 800 ; 𝑟 = 0.15 ; = 3 ; 𝑃 = ?
𝑃 = 800𝑒 (0.15)(3)
𝑷 = 𝟏𝟐𝟓𝟒. 𝟔𝟓 𝑷𝒆𝒔𝒐𝒔
2. Seojun decided to open a savings account for his future. He invested 10,000 Pesos at
an annual interest rate of 5% compounded continuously. Calculate the amount after
10 years.
When 𝐶 = 10,000 ; 𝑟 = 0.05 ; = 10 ; 𝑃 = ?
𝑃 = 10,000𝑒 (0.05)(10)
𝑷 = 𝟏𝟔, 𝟒𝟖𝟕. 𝟐𝟏 𝑷𝒆𝒔𝒐𝒔
3. Jung- Kyung deposited a principal of 6,000 pesos into her newly opened savings
account. The account is earning at an annual interest rate of 2% compounded
continuously. In 2 years what would be the amount of the money?
When 𝐶 = 6000 ; 𝑟 = 0.02 ; = 2 ; 𝑃 = ?
𝑃 = 6,000𝑒 (0.02)(2)
𝑷 = 𝟔, 𝟐𝟒𝟒. 𝟖𝟔 𝑷𝒆𝒔𝒐𝒔
4. An amount of Rs. 2340 is deposited in a bank paying an annual interest rate of 3.1%
compounded continuously. Find the balance after 3 years.
When 𝐶 = 2340 ; 𝑟 = 0.031 ; = 3 ; 𝑃 = ?
DEPARTMENT OF COMPUTER ENGINEERING
, DIFFERENTIAL EQUATION INSTRUCTIONAL MATERIALS
PROBLEM SETS
TOPIC: CONTINUOUS COMPOUND INTEREST
𝑃 = 𝐶𝑒 𝑟𝑡
𝑃 = 2340𝑒 0.031(3)
𝑷 = 𝑹𝒔. 𝟐𝟓𝟔𝟖. 𝟎𝟔
5. A principal of 1000 Euros is invested at a constant annual rate of 8%. Interest earned
is compounded continuously. Find the accured amount after 25 years.
When 𝐶 = 100,000 ; 𝑟 = 0.08 ; = 25 ; 𝑃 = ?
𝑃 = 𝐶𝑒 𝑟𝑡
𝑃 = 1000𝑒 0.08(25)
𝑷 = 𝟕𝟑𝟖𝟗. 𝟎𝟔 𝑬𝒖𝒓𝒐𝒔
AVERAGE
1. Deok-sun opened a savings account and deposited 50,000 Pesos as principal. The
account earns 7% interest, compounded continuously. What is the balance after 84
months and a half? How much is the interest earned?
When 𝐶 = 50,000 ; 𝑟 = 0.07 ; = 7.5 ; 𝐼 = ?
𝑃 = 50,000𝑒 (0.07)(7.5)
𝑃 = 84,522.94 𝑝𝑒𝑠𝑜𝑠
Interest earned:
𝐼 = 84,522.94 − 50,000
𝑰 = 𝟑𝟒, 𝟓𝟐𝟐. 𝟗𝟒
2. Taek invested 1,000 Pesos at 0.15% interest, compounded continuously. How much
is the balance after 3 years? How much is the interest accrued?
When 𝐶 = 100,000 ; 𝑟 = 0.15 ; = 3 ; 𝐼 = ?
𝑃 = 1000𝑒 (0.15)(3)
DEPARTMENT OF COMPUTER ENGINEERING
PROBLEM SETS
TOPIC: CONTINUOUS COMPOUND INTEREST
CONTINUOUS COMPOUND INTEREST
PROBLEM SET
General Formula: 𝑷 = 𝒄𝒆𝒓𝒕
EASY
1. Suho opened a savings account and deposited 800.00 Pesos as principal. The
account earns 15% interest, compounded continuously. What is the balance
after 3 years?
When 𝐶 = 800 ; 𝑟 = 0.15 ; = 3 ; 𝑃 = ?
𝑃 = 800𝑒 (0.15)(3)
𝑷 = 𝟏𝟐𝟓𝟒. 𝟔𝟓 𝑷𝒆𝒔𝒐𝒔
2. Seojun decided to open a savings account for his future. He invested 10,000 Pesos at
an annual interest rate of 5% compounded continuously. Calculate the amount after
10 years.
When 𝐶 = 10,000 ; 𝑟 = 0.05 ; = 10 ; 𝑃 = ?
𝑃 = 10,000𝑒 (0.05)(10)
𝑷 = 𝟏𝟔, 𝟒𝟖𝟕. 𝟐𝟏 𝑷𝒆𝒔𝒐𝒔
3. Jung- Kyung deposited a principal of 6,000 pesos into her newly opened savings
account. The account is earning at an annual interest rate of 2% compounded
continuously. In 2 years what would be the amount of the money?
When 𝐶 = 6000 ; 𝑟 = 0.02 ; = 2 ; 𝑃 = ?
𝑃 = 6,000𝑒 (0.02)(2)
𝑷 = 𝟔, 𝟐𝟒𝟒. 𝟖𝟔 𝑷𝒆𝒔𝒐𝒔
4. An amount of Rs. 2340 is deposited in a bank paying an annual interest rate of 3.1%
compounded continuously. Find the balance after 3 years.
When 𝐶 = 2340 ; 𝑟 = 0.031 ; = 3 ; 𝑃 = ?
DEPARTMENT OF COMPUTER ENGINEERING
, DIFFERENTIAL EQUATION INSTRUCTIONAL MATERIALS
PROBLEM SETS
TOPIC: CONTINUOUS COMPOUND INTEREST
𝑃 = 𝐶𝑒 𝑟𝑡
𝑃 = 2340𝑒 0.031(3)
𝑷 = 𝑹𝒔. 𝟐𝟓𝟔𝟖. 𝟎𝟔
5. A principal of 1000 Euros is invested at a constant annual rate of 8%. Interest earned
is compounded continuously. Find the accured amount after 25 years.
When 𝐶 = 100,000 ; 𝑟 = 0.08 ; = 25 ; 𝑃 = ?
𝑃 = 𝐶𝑒 𝑟𝑡
𝑃 = 1000𝑒 0.08(25)
𝑷 = 𝟕𝟑𝟖𝟗. 𝟎𝟔 𝑬𝒖𝒓𝒐𝒔
AVERAGE
1. Deok-sun opened a savings account and deposited 50,000 Pesos as principal. The
account earns 7% interest, compounded continuously. What is the balance after 84
months and a half? How much is the interest earned?
When 𝐶 = 50,000 ; 𝑟 = 0.07 ; = 7.5 ; 𝐼 = ?
𝑃 = 50,000𝑒 (0.07)(7.5)
𝑃 = 84,522.94 𝑝𝑒𝑠𝑜𝑠
Interest earned:
𝐼 = 84,522.94 − 50,000
𝑰 = 𝟑𝟒, 𝟓𝟐𝟐. 𝟗𝟒
2. Taek invested 1,000 Pesos at 0.15% interest, compounded continuously. How much
is the balance after 3 years? How much is the interest accrued?
When 𝐶 = 100,000 ; 𝑟 = 0.15 ; = 3 ; 𝐼 = ?
𝑃 = 1000𝑒 (0.15)(3)
DEPARTMENT OF COMPUTER ENGINEERING
