Peter deposited $8,975 into a savings account 21 years ago. The account has an interest rate of 3.8% and the balance is currently $19,909.20. How often does the interest compound?

Question

anonymous · Answer

daily

monthly

quarterly

annually 

(answer choices)

jamesj · Answer

The easiest way to do this is to calculate for each option until you find an answer that matches the final balance.

For example, if it compounded annually, then the amount would be
$$ 8975(1+.038)^21 $$ Is that equal to 19,909.2?

jamesj · Answer

**correction: $ 8975(1+.038)^{21} $

anonymous · Answer

so would it be daily monthly quarterly  or annually?

jamesj · Answer

Keep calculating and see.

anonymous · Answer

i don't get it..

jamesj · Answer

If it money were compounded quarterly, then what is the expression for the value of $8,975 at the end of 21 years?

anonymous · Answer

it'd be yearly?

jamesj · Answer

I wrote down above the expression for annual or yearly compounding:
$$ 8975(1+0.038)^{21} $$ That is equal to $19,641.70, so that's not the answer.

Now what is the expression if the amount is compounded quarterly?

anonymous · Answer

okay if its quaterly where do i put 24 at? like what do i multiply that by?

jamesj · Answer

What's the value of $1 at 3.8% compounded quarterly at the end of one year?  It is
$$ $1 . (1 + \frac{0.038}{4})^4 $$
Make sense?

jamesj · Answer

If so, then the value of $8975 at 3.8% compounded quarterly at the end of 21 years is
$$ $8975(1 + \frac{0.038}{4})^{21 \times 4 } $$

anonymous · Answer

ohhh okay lol