Question 1153297: how long will it take to save $20,000 by making deposits of $100 at the end of every month into an account earning interest at 6% compounded quarterly?
Answer by ikleyn(52847)   (Show Source):
You can put this solution on YOUR website! .
It works by the same way, as if the account is compounded quarterly.
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 deposit; r is the quarterly percentage yield presented as a decimal;
n is the number of deposits (= the number of quarters, in this case).
Under the given conditions, P = 100; r = 0.06/4. So, according to the formula (1), you get at the end of the n-th quarter
FV =  =  .
You want to find n from the inequality
>= 20000.
Then
 >=  = 3
 >= 4
n*log(1.015) >= log(4)
n >=  = 93.11
The preliminary ANSWER is 94 quarters, or 23 years and 2 quarters.
Let's check it. After 93 quarters, the amount will be
FV =  = 19955.95.
So, actually 93 quarters and 1 month is enough to get $20000.
The final answer. 93 quarters and 1 month, or 23 years and 4 months.
Solved.
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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.
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