Question

How much more would you earn in the first investment than in the second​ investment? ​$22 comma 000 invested for 30 years at 12​% compounded annually ​$22 comma 000 invested for 30 years at 6​% compounded annually You would earn ​$ nothing more on the first investment than in the second investment. ​(Round to the nearest dollar as​ needed.)

Answer 1

Therefore I would earn $532,761 more on the first investment than in the second investment.

Explanation:

The formula of compound interest

`A=P(1+r)^n`

Compound interest
`I=A-P`

A= Amount after n years

P= Principal

r=Rate of interest

n= Number of years

First investment,

P₁=$22,000, r=12%=0.12 and n=30 years

`A_1= 22,000(1+0.12)^(30)`

=659,118.28

≈$659,118

`I_1`=
`A_1`-P₁

=$(659,118-22,000)

=$637,118

Second investment,

P₂=$22,000, r=6%=0.06 and n=30 years

`A_1= 22,000(1+0.06)^(30)`

=126,356.81

≈$126,357

`I_2`=
`A_2`-P₂

=$(126,357-22,000)

=$104357

`I_1-I_2`

=$(637,118-104,357)

=$532,761

Therefore I would earn $532,761 more on the first investment than in the second investment.