Suppose
At the same time, we can write
Note that (just reverse the sum). Let's pair the first terms of
and
, and the second, and the third, and so on:
Now, each grouped term in the sum on the right side adds to 151. There are 52 grouped terms on that same side (because there are 50 numbers in the range of integers 51-100, plus 50 and 101), which menas
But , as we pointed out, so
wheee
Compute each option
option A: simple interest
simple interest is easy
A=I+P
A=Final amount
I=interest
P=principal (amount initially put in)
and I=PRT
P=principal
R=rate in decimal
T=time in years
so given
P=15000
R=3.2% or 0.032 in deecimal form
T=10
A=I+P
A=PRT+P
A=(15000)(0.032)(10)+15000
A=4800+15000
A=19800
Simple interst pays $19,800 in 10 years
Option B: compound interest
for interest compounded yearly, the formula is
where A=final amount
P=principal
r=rate in decimal form
t=time in years
given
P=15000
r=4.1% or 0.041
t=10
use your calculator
A=22418.0872024
so after 10 years, she will have $22,418.09 in the compounded interest account
in 10 years, the investment in the simple interest account will be worth $19,800 and the investment in the compounded interest account will be worth$22,418.09