Question

I need help with D, i’m confused on it.

Answer 1

Explanation:

`A=P(1+(r)/(n))^{nt`

A = future value ($)

P = principal (orignal amount - $400)

R = rate (written as a decimal - 3%/100= 0.03)

N = compound (yearly - 1)

T = number of years (0, 5, 10, 15)

Now, substitute each number into the formula and record them in the table.

0 years:

`A=P(1+(r)/(n))^(nt)\\\\A=400(1+(0.03)/(1))^(1*0)\\\\A=400(1+(0.03)/(1))^0 < ==any\ number\ raised\ to\ zero=1\\\\A=400(1)\\\\A=\$400`

5 years:

`A=P(1+(r)/(n))^(nt)\\\\A=400(1+(0.03)/(1))^(1*5)\\\\A=400(1+(0.03)/(1))^(5)\\\\A=400(1+{0.03})^(5)\\\\A=400({2.03})^(5)\\\\A=400({1.1593})\\\\A=\$463.72 < ==round\ to\ the\ nearest\ dollar\\\\A=\$464`

10 years:

`A=P(1+(r)/(n))^(nt)\\\\A=400(1+(0.03)/(1))^(1*10)\\\\A=400(1+(0.03)/(1))^(10)\\\\A=400(1+{0.03})^(10)\\\\A=400({1.03})^(10)\\\\A=400({1.3439})\\\\A=\$537.56 < ==round\ to\ the\ nearest\ dollar\\\\A=\$538`

15 years:

`A=P(1+(r)/(n))^(nt)\\\\A=400(1+(0.03)/(1))^(1*15)\\\\A=400(1+(0.03)/(1))^(15)\\\\A=400(1+{0.03})^(15)\\\\A=400({1.03})^(15)\\\\A=400({1.5579})\\\\A=623.16 < ==round\ to\ the\ nearest\ dollar\\\\A=\$623`

20 years:

`A=P(1+(r)/(n))^(nt)\\\\A=400(1+(0.03)/(1))^(1*20)\\\\A=400(1+(0.03)/(1))^(20)\\\\A=400(1+{0.03})^(20)\\\\A=400({1.03})^(20)\\\\A=400({1.8061})\\\\A=722.44 < ==round\ to\ the\ nearest\ dollar\\\\A=\$722`

Note that since we are rounding, answers may vary by a dollar or two.

Hope this helps!