Question

I really need help with this. Its frustrating me.
Earnest opens a savings account with $5,000. He deposits $900 each year into the account that compounds quarterly and has a 0.75% interest rate. What will his account total be in 5 years?

$9,771.94

$12,649.12

$10,706.30

$23,515.14

Answer 1

Please please help

Answer 2

c

Answer 3

how did you get that?

Answer 4

im on google right now i copy pasted your question

Answer 5

can you paste how that person did that problem?

Answer 6

Once you have comprehensible information, you can just piece it together.

"account that compounds quarterly and has a 0.75% interest rate"

What does that mean?
Is the Annual rate 0.75%?
Is the Quarterly rate 0.75%?

If it had said, "compounds at a quarterly interest rate of 0.75%" that would have been clear.

Let's assume it's a quarterly rate of 0.75%

i = 0.0075 -- The quarterly interest rate.
r = 1+i = 1.0075 -- The Quarterly accumulation factor

Now building!

(5000r^4 + 900) - One year
((5000r^4 + 900)r^4 + 900) - Two years
(((5000r^4 + 900)r^4 + 900)r^4 + 900) - Three years
((((5000r^4 + 900)r^4 + 900)r^4 + 900)r^4 + 900) - Four years
(((((5000r^4 + 900)r^4 + 900)r^4 + 900)r^4 + 900)r^4 + 900) - Five years

Not very pretty, is it? A little algebra...

5000r^20 + 900r^16 + 900r^12 + 900r^8 + 900r^4 + 900 - Five years - Much nicer.

4100r^20 + (900r^20 + 900r^16 + 900r^12 + 900r^8 + 900r^4 + 900) - Five years - Interesting.

4100r^20 + 900(r^20 + r^16 + r^12 + r^8 + r^4 + 1) - Five years - Better.

This is the fun one!

\(4100r^{20} + 900\left(\dfrac{1 - r^{24}}{1 - r^{4}}\right)\) - Five years - THAT was awesome. You DO need to know how to create the sum of a finite geometric series.

Note: This is building your own formula for the specific circumstance. It is not required to memorize what formula to use. Get good at creating them.

Note: Not everyone agrees with my opinion on this matter. Your algebra has to be super sharp and that seems like to great a requirement for some.

Answer 7

where did the 4100 come from? and dont you have to reduce the interest rate 0.0075/4

Answer 8

?

Answer 9

"where did the 4100 come from?"

The initial payment is 5000. Since all the other payments were 900, I grabbed 900 of the initial deposit for the big, fancy formula, leaving 4100 by itself at the beginning.

" and dont you have to reduce the interest rate 0.0075/4"

You must pay better attention. I addressed this issued quite directly up front. Your problem statement is not clear on this issue. I ASSUMED that 0.75% was the quarterly rate. If it is somehow clear that this is not the case, you will have to deal with that. The formulation is the same. This is why I used 'r' and 'i', so that you could substitute any applicable value.

Answer 10

ok. thanks.

Answer 11

You can see it clearly on the second to last equation. One of the 900s and the 4100 have the same exponent on their respective accumulation factors - indicating they occur at the same time.

Answer 12

can you help with another one?

Answer 13

What was the answer?

Answer 14

@chelseachels