Respuesta :
ANSWER
You will earn $1903593 in the first investment than the second investment
EXPLANATION;
Given that;
For the first investment;
Prinicipal = $23, 000
time = 40 years
interest rate = 12%
For the second investment
Principal = $23, 000
time = 40 years
interest rate = 6%
Follow the steps below to find the amount of each investment after 40 years
Note that; the investment was compounded annually
Hence, n = 1
Write the compound interest formula
[tex]\text{ A = P \lparen 1 + }\frac{\text{ r}}{\text{ n}})^{n\times\text{ t}}[/tex]For the first investment
[tex]\begin{gathered} \text{ A = 23000 \lparen 1 + }\frac{0.12}{1})^{1\times40} \\ \text{ A = 23000 \lparen1 + 0.12\rparen}^{40} \\ \text{ A = 23000\lparen1.12\rparen}^{40} \\ \text{ A = 23000 }\times\text{ 93.050} \\ \text{ A = \$2140150} \end{gathered}[/tex]For the second investment
[tex]\begin{gathered} \text{ A = P \lparen 1 + }\frac{\text{ r}}{\text{ n}})^{n\times t} \\ \text{ A = 23000 \lparen 1 + }\frac{0.06}{1})^{1\times40} \\ \text{ A = 23000 \lparen1 + 0.06\rparen}^{40} \\ \text{ A = 23000 \lparen1.06\rparen}^{40} \\ \text{ A = 23000}\times10.285 \\ \text{ A = \$ 236555} \end{gathered}[/tex]
Subtract the total amount realized in investmment 2 from investment 1
So, we have
[tex]\text{ \$2140150 - \$236555 = \$1903595}[/tex]Therefore, you will earn $1903593 in the first investment than the second investment
