Question

You wish to make an

Answer 1

Using the interest formulas, it is found that the values of the investment are given as follows:

• Using simple interest, the value will be of $34,000.

• Using compound interest, the value will be of $144,461.

• Using continuous compounding, the value will be of $148,002.

Simple Interest

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

$A(t) = P(1 + rt)$

In which:

• P is the initial amount.

• r is the interest rate, as a decimal.

In this problem, we have that the parameters are as follows:

P = 9000, r = 0.07, t = 40.

Hence:

$A(t) = 9000(1 + 0.07 x 40) = 34200$

Compound interest

$A(t) = P\left(1 + \frac{r}{n}\right)^{nt}$

n is the number of compounding, for quarterly n = 4, then:

$A(t) = 9000\left(1 + \frac{0.07}{4}\right)^{4 \times 40}$

$A(t) = 144461$

Continuous compounding

$A(t) = Pe^{rt}$

Hence:

$A(t) = 9000e^{0.07 \times 40} = 148002$

More can be learned about the interest formulas at brainly.com/question/25296782

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