Question

Samantha puts an initial $500 into a savings account. The account has a 4% annual compound interest rate. What is the function that best represents Samantha's account and how much does she have in savings after 5 years? Round your answer to the nearest dollar.
Hint: Use the formula, f(x) = P(1 + r)x.

Answer 1

f(x) = 500(1.4)x, $2,689
f(x) = 500(0.04)x, $512
f(x) = 500(1.04)x, $608
f(x) = 500(1.04)x, $5

Answer 2

I will fan and give a medal please help me

Answer 3

f(x) = 500(1.4)x, $2,689
f(x) = 500(0.04)x, $512
f(x) = 500(1.04)x, $608
f(x) = 500(1.04)x, $5

Answer 4

Are these given answers to choose from?

Answer 5

Yes

Answer 6

But I have no idea where to start

Answer 7

First I thought that it would be f(x)=500(40%)^5

Answer 8

Okay well, lets think of what we already know. Using the hint and the given answers we already know that P represents the amount Samantha put in already. Which is $500 right?

Answer 9

Now in the hint it shows to add R to 1. What do you think R represents?

Answer 10

Are you sure that in the parenthesis of hint you add 1 to r?

Answer 11

I don't understand

Answer 12

What is r

Answer 13

Start with P amount and r interest rate. r is written as a decimal.
For example, if the interest rate is 5%, you write it as 0.05

After 1 year, you have P(1 + r)
After 2 years , you have P(1 + r)(1 + r) = P(1 + r)^2
After 3 years, you have P(1 + r)^2(1 + r) = P(1 + r)^3
After 4 years, you have P(1 + r)^3(1 + r) = P(1 + r)^4
If you follow this pattern, after x years, you have

P(1 + r)^x

Notice that this is the formula the problem gives you in the hint.
Now replace P with 500 and r with 0.04, but leave x in.
What formula do you have now?

Finally use the new formula with x = 5 and evaluate it.

Answer 14

Thank you so much foryour help #mathstudent55 how do i give you a medal

Answer 15

You're welcome.
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