WORD PROBLEMS ON COMPOUND INTEREST

Problem 1 :

You invest $2,000 into an account that pays 4% interest and is compounded monthly. 

a. Write a model that represents this situation.

b. Using your model from part a, how much money will be in the account after 5 years? After 20 years?

Solution:

a.

Given, P = $2,000, r = 4% = 0.04, n = 12

b. 

After 5 years,

t = 5

After 20 years,

t = 20

Problem 2 :

Samantha just won an AAFES sweepstake and has been given $1,000,000!!! The only catch is she is not allowed to spend any of it for 15 years, but she is allowed to invest it. She found certificate of Deposit account that will pay her 5.25% annual interest compounded daily.

a. Write a model that represents this situation.

b. Using the model to help, calculate how much interest she gained during those 15 years.

Solution:

a)

b)  Interest = Amount - Principal

= 1142300 - 1000000

= 142300

Write a model for each scenario and use the model to calculate the balance for the given number of years.

Problem 3 :

You deposit $500 in an account that pays 8% annual interest compounded monthly. How much will you have after 15 years?

Solution:

Given, P = $500, r = 8%

Compounding monthly, then n = 12 

n = 12, t = 15

Problem 4 :

You deposit $575 in an account that pays 4% annual interest compounded continuously. How much will you have after 5 years?

Solution:

Given, P = $575, r = 4%, n = 1, t = 5

Problem 5 :

You deposit $3,000 in an account that pays 3.28% annual interest. Find the balance after 5 years if the interest is compounded semi-annually. How much would you have if the interest was compounded daily for five years?

Solution:

Given, P = $3000, r = 3.28%, n = 2, t = 5

Problem 6 :

Jasmine invests $2,658 in a retirement account with a fixed annual interest rate of 9% compounded continuously. What will the account balance be after 15 years?

Solution:

Compound interest :

A = Pe^rt

P = $2658, r = 9% = 0.09, t = 15

e = 2.7183 (Napier's number)

A = 2658(2.7183)^0.09(15)

A = $10,253

Hence, account balance after 15 years is approximately $10,253.

Problem 7 :

Maria invests $6,154 in a savings account with a fixed annual interest rate of 8% compounded continuously. What will the account balance be after 10 years?

Solution:

Given, P = $6154, r = 8% = 0.08, t = 10

A = P₀ e^rt

A = 6154 (2.71)^0.08(10)

= 6154 (2.71)^0.8

= 6154 (2.22)

= 13662.8

The balance after 10 years is $13663

Problem 8 :

Ryan invests a sum of money in a savings account with a fixed annual interest rate of 4.31% compounded 12 times per year. After 10 years, the balance reaches $12,855.94. What was the amount of the initial investment?

Solution:

Given, A = $12,855.94, Rate r = 4.31%, Time t = 10 yrs

Compounded 12 times per year we have to find amount of initial investment

Hence, initial investment = $8570.62.

Problem 9 :

Ndiba invests a sum of money in a savings account with a fixed annual interest rate of 4.61% compounded 3 times per year. After 6 years, the balance reaches $5,485.85. What was the amount of the initial investment?

Solution:

Given, r = 4.61% = 0.0461 per year

A = $5485.85

Hence, amount of initial investment  = $4168.99