Question

Aryana wants to invest $43,000. She has two options. Option A gives her 6% compounded quarterly. Option B gives her 6% simple interest annually. Which option earns higher interest after 3 years and by how much?

Answer 1

Answer:

Option A earns higher interest($84115.58)

the difference in interest between the two option is  $197.9

Step-by-step explanation:

 In the problem we are going to apply both the simple interest formula and compound interest formula and compare which has the best/higher returns

Given data

Principal P= $43,000

Rate r= 6%= 0.06

time t= 3years

n= 4 (applicable for compound interest compounded quarterly)

solving for option A gives her 6% compounded quarterly

the compound interest formula is

$A= P(1+\frac{r}{n} )^n^t\\A= 43000(1+\frac{0.06}{4} )^{4} ^*^3$

$A=43000(1+0.015)^{12} \\A=43000(1.015)^{12} \\A=43000*1.1956\\A= 51411.58$

Interest is $A-P= 51411.58-43000= 8411.58$=$8411.58

solving for option B  which gives her 6% simple interest annually

the simple interest formula is

$A=P(1+r)^{t} \\A=43000(1+0.06)^3\\A=43000(1.06)^3\\A=43000*1.191\\A= 51213.68$

Interest is$A-P=51213.68-43000= 8213.68$= $8213.68

calculating the diference in interest between the two options we have

$8411.58-8213.68= 197.9$= $197.9

Option A earns higher interest