SOLUTION: Find i​ (the rate per​ period) and n​ (the number of​ periods) for the following annuity. Quarterly deposits of $1,000 are made for 7 years into an annuity that pays 9%

Algebra.Com
Question 1177395: Find i​ (the rate per​ period) and n​ (the number of​ periods) for the following annuity.
Quarterly deposits of $1,000 are made for 7 years into an annuity that pays 9% compounded quarterly.
I = ?
I need to see all the calculations for this question to understand please!
Homework question from Hans Beauvoir

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

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


    FV = ,    (1)


where  FV is the future value of the account;  P is the quarterly payment (deposit); 
r is the quarterly percentage yield presented as a decimal (it is " i " , in your terminology);
n is the number of deposits (= the number of years multiplied by 4, in this case).


Under the given conditions, P = 1000;  r = 0.07/4 = 0.0175;  n = 4*7 = 28.   <<<===---  it is partial answer to your questions 


So, according to the formula (1), you get at the end of the 7-th year


    FV =  =  = $35,737.88.


Note that you deposit only  4*7*$1000 = $28,000.  The rest is what the account earns/accumulates in 7 years.

Solved, answered and explained.

-----------------

On Ordinary Annuity saving plans,  see the lessons
    - Ordinary Annuity saving plans and geometric progressions
    - Solved problems on Ordinary Annuity saving plans
in this site.

The lessons contain  EVERYTHING  you need to know about this subject,  in clear and compact form.

When you learn from these lessons,  you will be able to do similar calculations in semi-automatic mode.


///////////


Do not forget to post your "THANKS" to me for my teaching.



RELATED QUESTIONS

Find the rate per period (i) and the number of periods (n) for the following situation:... (answered by Alan3354)
Find the length of time required for an investment of $1500 to amount to $2000 at rate of (answered by ikleyn)
Find the length of time required for an investment of $1500 to amount to $2000 at a rate... (answered by MathTherapy)
Give the number of periods, n, and the interest rate per period, i, for the following... (answered by jorel1380)
Suppose you invest $82,000.00, and it earns 9% annual interest, compounded 12 times per... (answered by josgarithmetic)
We have used the formula A = R (1 + i)n − 1 i to find the future value of... (answered by MathLover1,MathTherapy,ikleyn)
Find the amount (future value) of the ordinary annuity. $1,400 per quarter for 5 yr at... (answered by Theo)
Use the compound interest formula P = A(1 + i)^n, where A is the original value of an... (answered by greenestamps)
A financial advisor recommends that a client deposit $2600 into a fund that earns 7.5%... (answered by ikleyn)