i need help with my math problems

Question

the bank offer a savings account that accrues simple interest annually based on an initial deposit of $500. if S(t) represents the money in the account at the end of t years and S(5)=575, white a function that could be used to determine the amount of money in the account over time?

Answer 1

Initial value is:

S(0) = 500

 

Since we're accruing simple interest, the amount of money at the end of t years is represented by:

 S(t) = 500(1 + i*t)

where i = interest rate and t = # of years

 

We know that S(5) = 575. We want to find i so we can find the general equation for the amount of money over time.

 

S(5) = 575 = 500(1 + 5i)

           1.15 = 1 + 5i

               0.15 = 5i

                i = 0.03 (so account accrues 3% interest per year)

 

Function: S(t) = 500(1 + 0.03t)