Question

How much more would you earn in the first investment than in the second investment?$23,000 invested for 40 years at 12% compounded annually$23,000 invested for 40 years at 6% compounded annuallyi Click the icon to view some finance formulas.You would earn $ more on the first investment than in the second investment.(Round to the nearest dollar as needed.)

Answer 1

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

`\text{ A = P \lparen 1 + }\frac{\text{ r}}{\text{ n}})^{n*\text{ t}}`

For the first investment

`\begin{gathered} \text{ A = 23000 \lparen 1 + }(0.12)/(1))^(1*40) \\ \text{ A = 23000 \lparen1 + 0.12\rparen}^(40) \\ \text{ A = 23000\lparen1.12\rparen}^(40) \\ \text{ A = 23000 }*\text{ 93.050} \\ \text{ A = \$2140150} \end{gathered}`

For the second investment

`\begin{gathered} \text{ A = P \lparen 1 + }\frac{\text{ r}}{\text{ n}})^(n* t) \\ \text{ A = 23000 \lparen 1 + }(0.06)/(1))^(1*40) \\ \text{ A = 23000 \lparen1 + 0.06\rparen}^(40) \\ \text{ A = 23000 \lparen1.06\rparen}^(40) \\ \text{ A = 23000}*10.285 \\ \text{ A = \$ 236555} \end{gathered}`

Subtract the total amount realized in investmment 2 from investment 1

So, we have

`\text{ \$2140150 - \$236555 = \$1903595}`

Therefore, you will earn $1903593 in the first investment than the second investment