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.
|
|
|
