Question

Roberta invested $600 into a mutual fund that paid 4% interest each year compounded annually. Write an exponential function of the form y=a(b)x to describe the value of the mutual fund then use that function to determine the value of the mutual fund in 15 years

Answer 1

y = 600*(1.04)^t

for t = 15: y = $1080.57

Explanation:

The exponencial function y = a(b)x have the following variables:

a: inicial value

b: rate of interest plus one

x: time invested

So, if the inicial value invested is 600, the rate is 4% and the time is 15 years, we have that the equation is:

y = 600*(1+0.04)^t = 600*(1.04)^t

And for time t = 15 years, we have that:

y = 600*(1.04)^15 = $1080.57

Answer 2

The exponential equation is A = 600(1.04)^15

The value of the mutual fund after 15 years is $1,081

Explanation:

The value of the mutual fund after the number of years can be represented using the compound interest equation below;

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

Where A is the value of the mutual fund after 15 years, P is the initial amount invested which is $600, r is the interest rate which is 4% or 0.04(4% = 4/100 = 0.04), n is the number of times we are compounding per year(which is 1 since it is a one time payment per year) and t is the number of years which is 15

Let's plug these values, we have;

A = 600(1 + 0.04/1)^15

A = 600(1.04)^15

A = $1,081 approximately