Lesson Find a value of regular deposits for an Ordinary Annuity saving plan

Find a value of regular deposits for an Ordinary Annuity saving plan

Problem 1

It is a classic Ordinary Annuity saving plan. The general formula is 


    FV = ,    


where  FV is the future value of the account;  P is the monthly payment (deposit); 
r is the monthly percentage yield presented as a decimal; 
n is the number of deposits (= the number of years multiplied by 12, in this case).


From this formula, you get for the monthly payment 


    P = .     (1)


Under the given conditions, FV = $600,000;  r = 0.05/12;  n = 20*12.  
So, according to the formula (1), you get for the monthly payment value


    P =  = 1459.74  (rounded to closest greater cent).


Answer.  The necessary monthly deposit value is $1459.74.


Note that of projected $600,000 the total of deposits you will be only  20*12 times $1459.74, 
i.e. 20*12*1459.74 = 350337.60 dollars. The rest 600000 - 350337.60 = 249662.40 is the interest,
which the account will earn/accumulate in 20 years.

Problem 2

This problem is about a quarterly payment for Ordinary Annuity saving plan.


The formula for the Ordinary Annuity saving plan is


f = ,


f is a future value
p is a monthly payment
r is an effective interest rate per time period
n is a number of time periods.


In your problem:


time periods are quarters.


f = 7700000
p = the quarterly deposit amount, which you want to find
r = 0.06/4
n = 14 years * 4 quarters = 56 payment periods


Formula becomes 7700000 = 


Express p from it to get:


    p =  = 88712.19  dollars.


The company should deposit $88712.19 quarterly in order to have $7,700,000 in 14 years at 6% per year compounded quarterly.


Interesting, that the company's total direct deposit will be only  $88712.19*4*14 = 4,967,883  dollars.

The rest is the interest which the account will earn.

Problem 3

It is a classic Ordinary Annuity saving plan. The general formula is 


    FV = ,    


where  FV is the future value of the account;  P is the monthly payment (deposit); 
r is the monthly percentage yield presented as a decimal; 
n is the number of deposits (= the number of years multiplied by 12, in this case).


From this formula, you get for the monthly payment 


    P = .     (1)


Under the given conditions, FV = $280,000;  r = 0.04/12;  n = 30*12.  
So, according to the formula (1), you get for the monthly payment 


    P =  = $403.43.


Answer.  The necessary monthly deposit value is $403.43.