Lesson Problems on discretely compounded accounts

Problems on discretely compounded accounts

Problem 1

Let p be the value under the problem's question, now unknown.


The formula for the future value of an one-time deposited amount is 

    f = p * (1 + r) ^ n,


where  f is a future value
       p is a  principal (one-time original deposit)
       r is an interest rate per time period as a decimal number
       n is the number of time periods.


In your problem:


       p is unknown;
       f = given future value of $7500;
       r = 4% annually (0.04 as a decimal);
       n = 6 annual periods = 6 years.


Formula becomes 

   76500 = .


It gives us the ANSWER

    p =  = 5927.36  dollars  (rounded to the closest greater cent).

Problem 2

Use the formula for discretely compounded account 

      f = p * (1 + r) ^ n


where f is the future value
      p is the principal (the deposited amount)
      r is the interest rate per time period, presented as a decimal
      n is the number of time periods.


Your time periods are quarters.


f = 39000 dollars;
r = 0.04/4 = 0.01;
n = 18 years * 4 quarters = 72 quarters.


Formula becomes 39000 = ,  which gives

    p =  =  = 19051.35  dollars  (rounded to the closest greater cent).    ANSWER

Problem 3

Use the formula for discretely compounded account 

      f = p * (1 + r) ^ n


where f is the future value
      p is the principal (the deposited amount)
      r is the interest rate per time period, presented as a decimal
      n is the number of time periods.


Your time periods are months.


f = 3000.
r = 0.03/12.
n = 10 years * 12 = 120 months.


Formula becomes 3000 = ,  which gives

    p =  = 2223.29  to the nearest cent.    ANSWER

Problem 4

Write equation for the future value 

    1350 = 


where X is your unknown, which is the value under the question.


From the equation,   X =  = 1235.44 dollars.    ANSWER

Problem 5

Write your governing equation to be a millionaire with the exponentially growing account


    1,000,000 =  = .


From this equation, find the initial amount to deposit

    x =  = 267848.32.


Round it to the closest greater dollar to get the 


ANSWER.  $267849.


CHECK.   = 1000002.54.   ! very good;  extremely nice !