COMPOUND INTEREST MATH PROBLEMS

Question

A person invests $2860 for 15 years in an account that earns 4.6% annual interest.

FIND THE DIFFERENCES BBETWEEN (IN DOLLARS):

 

1. compounding interest
semiannually and annually

 

2. compounding interest
quarterly and semiannually

 

3. compounding interest
monthly and quarterly

 

4. compounding interest
daily and monthly

 

5. compounding interest
continuously and daily

Answer 1

A person invests $2860 for 15 years in an account that earns 4.6% annual interest.

 

The way your question is phrased the interest would be compounded

once per year.  Based on the questions you are asked to solve, I will

assume the world "annually" should not be in the above sentence.

 

Your problem utilizes the compound interest formula:

A = p(1+r/n)^nt

A = future amount

p = principal or initial investment = 2860

r = interest rate as decimal = .046

n = number of times compounded each year

t = time in years = 15

 

1.  Semiannually means interest compounded 2 times yearly so n=2

     A = 2860(1+.046/2)²⁽¹⁵⁾ = 2860(1.023)³⁰ = 5657.64

    

     Annually means interest compounded 1 time yearly so n=1

     A = 2860(1+.046/1)¹⁽¹⁵⁾ = 2860(1.046)¹⁵ = 5614.89

 

     The difference is 5657.64 - 5614.89 = $42.75   with semiannually

     being the larger interest earned.

 

2.  Quarterly:  Interest compounded 4 times per year, n=4

     A = 2860(1+.046/4)⁴⁽¹⁵⁾

 

    Semiannually:  Refer to problem 1:  A = 5657.64

 

    Work the quarterly formula on calculator and find the difference.

 

3.  Monthly:  Interest compounded 12 times per year, n=12

     A = 2860(1 + .046/12)¹²⁽¹⁵⁾

 

     Quarterly:  Refer to problem 2 for quarterly final amount.

 

4.  Daily:  Interest compounded 365 times per year, n=365

     A = 2860(1 + .046/365)^365(15)

 

     Monthly:  Refer to problem 3 for monthly final amount.

 

5.  Interest compounded continually uses a different formula.

     A = Pe^rt

     e is Eulers number... approximately 2.7183... find it on calculator

 

    A = 2860e^.046(15)

    A = $5702.03

    

    For daily compounding amount refer to problem 4.

 

Answer 2

For the following problems, use the compound interest formula

 

A = P(1 + (r / n))^nt

 

where:

A = amount accumulated

P = investment

r = interest rate (in decimal)

n = number of times compounded per year

t = time (in years)

 

 

Given:

P = 2680

t = 15

r = 0.046

 

 

You will use these known values for each problem to find the value of A.  Then, you will find the difference between the 2 A's for each problem.   Use the following values of n for each problem given the conditions

 

semiannually      n=2

annually             n=1

quarterly            n=4

monthly             n=12

daily                  n=365

 

continuously     use the formula     A = Pe^rt.   Note that there is no n for this condition.