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

A.) f(x) = 500(1.4)x, $2,689
B.) f(x) = 500(0.04)x, $512
C.) f(x) = 500(1.04)x, $608
D.) f(x) = 500(1.04)x, $527

Answer 1

In the equation, P would be the principle, or the amount in this case, multiplied by the annual rate raised by the number of years. 4% in decimal form would be .04, adding 1 to it includes the total principle plus the 4%, if you just multiplied by .04 you would be taking 4% of the $500. The answer is C.

Answer 2

The best and most correct answer among the choices provided by your question is the third choice or letter C. The equation would be f(x) = 500(1.04)x, $608.

I use a bit of a different looking formula.

A(t)=P(1+r/n)^nt

P=amount of money. (500)
r= rate (in decimal. 4%=0.04)
n=number of times per year (1 in this problem)
t=amount of time. (5 years)

Plugged in it looks like this:

A(t)=500 (1+ 0.04/1)^1x5

Then I put it into my calculator like this:

0.04/1+ 0.04

Then add one to the above answer:

0.04+1=1.04

Then raise the above answer to the 1x5:

1.04^5=1.2166......

Then multiply the above answer by 500:

1.2166.... x 500=608.3264512

She has $608 after 5 years.