Question 1

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

Question 2

SOLUTION

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

$\begin{gathered} A=P(1+(r)/(n))^(nt) \\ 25,200=24,000(1+(r)/(4))^^(4*3.2) \\ 25,200=24,000(1+(r)/(4))^(12.8) \\ (1+(r)/(4))^(12.8)=(25200)/(24000) \\ (1+(r)/(4))^(12.8)=1.05 \\ ((4+r)/(4))^(12.8)=1.05 \end{gathered}$

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%

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