Answer:
<em>400(1-0.05)^3400(1−0.05)^3
</em>
Step-by-step explanation:
A 5\%5%5, percent annual interest means the balance grows by a factor of 105\%105%105, percent each year, which is the same as 1.051.051, point, 05.
If we start with \$400$400dollar sign, 400 and keep multiplying by 1.051.051, point, 05 we get 400\cdot 1.05^3400⋅1.05
3
400, dot, 1, point, 05, start superscript, 3, end superscript, so this expression does give the correct amount.
Let's check the other expressions.
400\cdot 1.05^3=400(1+0.05)(1+0.05)(1+0.05)400⋅1.05
3
=400(1+0.05)(1+0.05)(1+0.05)400, dot, 1, point, 05, start superscript, 3, end superscript, equals, 400, left parenthesis, 1, plus, 0, point, 05, right parenthesis, left parenthesis, 1, plus, 0, point, 05, right parenthesis, left parenthesis, 1, plus, 0, point, 05, right parenthesis
So 400(1+0.05)(1+0.05)(1+0.05)400(1+0.05)(1+0.05)(1+0.05)400, left parenthesis, 1, plus, 0, point, 05, right parenthesis, left parenthesis, 1, plus, 0, point, 05, right parenthesis, left parenthesis, 1, plus, 0, point, 05, right parenthesis also gives the correct balance.
We can also take this approach:
Time Addition Balance
Beginning 000 400400400
After 111 year 400\cdot 0.05=20400⋅0.05=20400, dot, 0, point, 05, equals, 20 400+20=420400+20=420400, plus, 20, equals, 420
After 222 years 420\cdot 0.05=21420⋅0.05=21420, dot, 0, point, 05, equals, 21 400+20+21=441400+20+21=441400, plus, 20, plus, 21, equals, 441
After 333 years 441\cdot 0.05441⋅0.05441, dot, 0, point, 05 400+20+21+441\cdot 0.05400+20+21+441⋅0.05400, plus, 20, plus, 21, plus, 441, dot, 0, point, 05
So:
400+ 400(0.05)+420(0.05)+441(0.05)400+400(0.05)+420(0.05)+441(0.05)400, plus, 400, left parenthesis, 0, point, 05, right parenthesis, plus, 420, left parenthesis, 0, point, 05, right parenthesis, plus, 441, left parenthesis, 0, point, 05, right parenthesis
also gives the correct balance.
The only expression that does not give the correct balance after 333 years is:
<em>400(1-0.05)^3400(1−0.05)^3
</em>
