A student has a savings account earning 9% simple interest. She must pay $1500 for first-semester tuition by September 1 and $1500 for second-semester tuition by January 1. How much must she earn in the summer (by September 1) to pay the first-semester bill on time and still have the remainder of her summer earnings grow to $1500 between September 1 and January 1?

  $2956.31  in total by september 1st

Explanation:

Using the formula A = P ( 1 + rt )

our given  Data:

Rate of simple interest = 9%

r = 0.03/12 per month

P= Money in the bank by Sep 1 and A= $1500

FOR t=4 means that there are four months between 1st September and 1st January

So, in order to have the remainder of summer earnings grow to $1500 between September 1 and January 1,

we have that  A = P ( 1 + rt )

1500 = P [1 +  .09(4/12)]

1500 = P (1 + .03) 1500 / 1.03 =

P= $1456.31  

This implies  that she  needs to earn 1500 + 1456.31 = $2956.31 during summer to ensure that t she will have enough money to pay first semester on time in september  and still have remainder of her earnings to grow by January 1st.

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