Question

What would the rate of interest have to be? Round to two decimal places

Answer 1

To solve this we would use the formula

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ where\text{ } \\ A=amount\text{ after time t = 24,000 + 1200 = \$25,200} \\ P=money\text{ invested = \$24,000} \\ r=interest\text{ rate = ?} \\ t=time\text{ in years = 3.2 years } \\ n=number\text{ of compounding = 4} \end{gathered}`

Applying we have

Continuing we have

`\begin{gathered} (4+r)/(4)=(1.05)^{(1)/(12.8)} \\ (4+r)/(4)=1.003819 \\ 4+r=4*1.003819 \\ r=4.0152760-4 \\ r=0.015276 \end{gathered}`

The rate becomes

`\begin{gathered} r=0.015276*100 \\ r=1.5276 \end{gathered}`

Hence r = 1.53%