Question

Which of the following represents the amount of dollars after $n$ years if there is an annual increment of $25\%$ on the principal amount of $\$18?$

• A. $\$18(0.25{)}^n$
• B. $\$18(1.25{)}^{(n-1)}$
• C. $\$18(1.25{)}^{(n+1)}$
• D. $\$18(1.25{)}^n$

Answer 1

The correct option is D $\$18(1.25{)}^n$

Given:
Initial principal amount $=\$18$
Annual increment $=25\%$

To Find:
Correct representation for the amount of money (in dollars) after $n$ years

$\bullet$ After $\underset{–}{1\text{year}}$, the amount of money becomes $=$ Amount at the start of the year $+$ $25\%$ of the amount at the start of the year

$=\$(18+25\%\text{of}18)$

$=\$(18+\frac{25\times 18}{100})$

$=\$18(1+\frac{25}{100})$

$=\$18(1+0.25)$

$=\$18(1.25{)}^{\underset{–}{1}}$

$\bullet$ After $\underset{–}{2\text{years}}$, the amount of money will become $=$ Amount after $1$ year $+$ $25\%$ of amount after $1$ year

$=\$\{18\left(1.25\right)+\frac{18\left(1.25\right)\times 25}{100}\}$

$=\$18\left(1.25\right)(1+0.25)$

$=\$18\left(1.25\right)\left(1.25\right)$

$=\$18(1.25{)}^{\underset{–}{2}}$
$.$
$.$
$.$

$\bullet$ Similarly, After $\underset{–}{n\text{years}}$ the amount of money will be $=\$18(1.25{)}^{\underset{–}{n}}$

Therefore, option (d.) is the correct one.