Question

If you invest $1250 in an account that earns 6% compounded quarterly, the amount you will have in the account, S(x), after x years is given by
S(x)=1250(1.015)^ 4x
Calculate the amount of money in the account, S(x), after 2, 4, 6, 8, and 10 years and the interest earned in the account.

Is this an exponential growth or decay function? How much more money would you earn in interest if you left the money in the account 10 years instead of 4 years? What is the S – intercept (y-intercept) for this function and what does it represent?

Answer 1

well, we know what S(x) is, since it's given, so, after , is simply a matter of x = 2,4,6,8,10, so

$\begin{array}{llrll} S(2)=1250(1.015)^{4(2)}&\implies &S(2)\approx 1408.12\\ S(4)=1250(1.015)^{4(4)}&\implies &S(4)\approx 1586.23\\ S(6)=1250(1.015)^{4(6)}&\implies &S(6)\approx 1786.88\\ S(8)=1250(1.015)^{4(8)}&\implies &S(8)\approx 2012.91\\ S(10)=1250(1.015)^{4(10)}&\implies &S(10)\approx 2267.52 \end{array}$

well, the tell-tale for Growth or Decay is the parenthesized term, namely the "rate of change", if it's greater than 1 is Growth, if it's less than 1 is Decay, in this case is greater than 1, is 1.015, so well, you know.

from 4 years to 10 years, how much more in interest?

well, first off let's take off the Principal of 1250 to see how much is in interest, hmmm for 4 years that'll be 336.23 and for 10 years that'll be 1017.52, so their difference is about 681.29.

what does the S-intercept mean?  Check the picture below.

when the graph touches the y-axis or S-axis if you wish, the time is 0 and the amount is, well, you can see it there.