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

Option A earns higher interest($84115.58)

the difference in interest between the two option is $197.9

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+(r)/(n) )^n^t\\A= 43000(1+(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