Question

Nelson took out a home loan that compounds interest semiannually. The following expression represents the payable amount after t years. 150,000(1.012)^2t
What is the annual rate of interest for this situation?
0.6%
2.4%
0.06%
1.2%

Answer 1

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\ 150,000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\to &2\\ t=years \end{cases}$

$\bf A=150000\left(1+\frac{r}{2}\right)^{2\cdot t}\implies A=150000\left(1+\frac{r}{2}\right)^{2 t} \\\\\\ \boxed{150000\left(1+\frac{r}{2}\right)^{2 t}~~~~=~~~~150000(1.012)^{2t}} \\\\\\ \left(1+\frac{r}{2}\right)=(1.012)\implies 1+\cfrac{r}{2}=1.012\implies \cfrac{r}{2}=0.012 \\\\\\ r=0.024\implies r\%=0.024\cdot 100\implies r=\stackrel{\%}{2.4}$

Answer 2

Answer:

its 2.4 if thats confusing

Step-by-step explanation: