Question

Suppose Diana places $4500 in an account that pays 8% interest compounded each year. Assume that no withdrawals are made from the account. Find the amount in the account at the end of one year.Find the amount in the account at the end of two years.Do not do any rounding.

Answer 1

The rule of the compounded interest is

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

A is the new amount

P is the initial amount

r is the rate in decimal

n is the number of periods per year

t is the time in years

Since the initial amount is $4500, then

P = 4500

Since the interset is 8% yearly, then

r = 8/100 = 0.0

n = 1

For 1 year t = 1, for two years t = 2

Let us find the new amount in the 2 cases

$\begin{gathered} A=4500(1+\frac{0.08}{1})^{(1)(1)} \\ A=4500(1.08) \\ A=4860 \end{gathered}$

The amount in the account at the end of one year is $4860

$\begin{gathered} A=4500(1+\frac{0.08}{1})^{(1)(2)} \\ A=4500(1.08)^2 \\ A=5248.8 \end{gathered}$

The amount in the account at the end of two years is $5248.8