Question

Arlo invested $4000 in an account that earns 5.5% interest, compounded annually. The formula for compound interest is A(t)=P(1+i)^t. How much did Arlo have in the account after 4 years?

Answer 1

Answer:

$ 4955.30 ( approx )

Step-by-step explanation:

The formula for compound interest is,

$A(t)=P(1+i)^t$

Where, P is the principal amount,

i is the rate per period,

t is the number of periods,

Here, P = $ 4000,

i = 5.5% = 0.055

t = 4 years,

By substituting the values,

The amount in the account after 4 years would be,

$A=4000(1+0.055)^4=4000(1.055)^4=4955.2986025\approx \ 4955.30$

Answer 2

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 4000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A=4000\left(1+\frac{0.055}{1}\right)^{1\cdot 4}\implies A=4000(1.055)^4\implies A\approx 4955.2986$