Question

10 an investment of $75,000 increases at a rate 12.5% per year. find the value of the investment after 30 years $1,438,883 $243,549 $256,825 $5,548,245

Explanation:

Step1: Identify the formula for compound growth

The formula for compound growth is $A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the number of years.
Here, $P = 875000$, $r = 0.125$ (since $12.5\%= \frac{12.5}{100}=0.125$), and $t = 30$.

Step2: Substitute the values into the formula

Substitute $P = 875000$, $r = 0.125$, and $t = 30$ into the formula $A = P(1 + r)^t$:
$$A=875000\times(1 + 0.125)^{30}$$
First, calculate $1+0.125 = 1.125$. Then we need to calculate $1.125^{30}$.

Step3: Calculate $1.125^{30}$

Using a calculator, $1.125^{30}\approx1.644464$.

Step4: Calculate the final amount $A$

Multiply $875000$ by $1.644464$:
$$A = 875000\times1.644464\approx1438886.$$
Among the given options, $\$1,438,883$ is the closest (due to possible rounding differences in the exponent calculation).

Answer:

$1,438,883$