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+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$150,000\\ r=rate\to r\%\to (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+(r)/(2)\right)^(2\cdot t)\implies A=150000\left(1+(r)/(2)\right)^(2 t) \\\\\\ \boxed{150000\left(1+(r)/(2)\right)^(2 t)~~~~=~~~~150000(1.012)^(2t)} \\\\\\ \left(1+(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

its 2.4 if thats confusing

Explanation: