Question

Hakim deposited $50 in a saving account earning 10% interest, compounded annually . To the nearest cent , how much interest will he earn in 2 years?

Answer 1

Answer:

$10.50

Step-by-step explanation:

(see attached for reference)

The formula for compound interest is:

A = P [1 + (r/n) ]^(nt)

where

A = Final amount

P = Principal = $50

r = Annual interest rate = 10% = 0.1

n = 1 (because compounded annually)

t = time = 2 years

substituting this into the equation:

A = P [1 + (r/n) ]^(nt)

= 50 [ 1 + (0.1/1) ] ^ [(1)(2)]

= 50 [ 1 + 0.1] ^ 2

= 50 (1.1)²

= $60.50

Interest = Final amount - Principal

=$60.50 - $50.00

=  $10.50

Answer 2

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 50\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases}$

$\bf A=50\left(1+\frac{0.10}{1}\right)^{1\cdot 2}\implies A=50(1.1)^2\implies A=60.5 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{earned interest}}{60.5 - 50\implies 10.5}~\hfill$