Question

-1 points My Notes A HarMathAP12 6.1.016.MI. student has a savings account earning 9% simple interest. She must pay $1600 for first semester tuition by September 1 and $1600 for second semester tuition by January 1. How much must she earn by September 1) to pay the first semester bill on time and still have the remainder of her summer earnings grow to $1600 between September 1 and January 17 (Round your answer to the nearest cent.) Need Help? Water Tante Tutar

Answer 1

Solution:-

Let us assume that the student needs to earn $ x in summer by September 1.

There are Four Months form Sep 1 to Jan 1

Simple Interest = 1/3 * 9 = 3%

After paying the first-semester bill of $ 1600 on time,

She has $ x - 1600 left.

This amount earns simple interest at 9% for 6 months so that it grows to

(x - 1600) * (1+ 0.09 *1/3) = (x-1600)*1.03

Now, since the remainder of her summer earnings grows to $1600 between September 1 and January 1, hence

(X-1600) * 1.03 = 1600 or, x-1600 = 1600/1.03 = 1553.4

So that x = 1600 + 1553.40 = 3153.4 (on rounding off to 2 decimal places).

This means that the student needs to earn $ 3153.4 in summer by September 1.