Q70. - Algebra 2

Question

70. GRID IN Suppose you deposit $500 in an account paying 4.5% interest compounded semi-annually. Find the dollar value of the account rounded to the nearest penny after 10 years.

Step-by-Step Solution

Answer

The dollar value of the account is $780.25.

Step 1. Given

Suppose you deposit $500 in an account paying 4.5% interest compounded semi-annually.

Step 2. To determine

Find the dollar value of the account rounded to the nearest penny after 10 years.

Step 3. Calculation

Given,

P = The principal amount = $500.

r = Interest rate = 4.5% = 0.045

n = The number of times compounded annually = 2 (because of semi-annually)

t = time = 10 years.

So, the dollar value of the account is:

$\begin{array}{l}A=P{\left(1+\frac{r}{n}\right)}^{nt}\\ A=500{\left(1+\frac{0.045}{2}\right)}^{2\left(10\right)}\\ A=780.254600342\\ A\approx 780.25\end{array}$

Hence, the dollar value of the account is $780.25.