Question

Q13 5.3 PHOTO ATTACHEED THANK YOUQUESTION 13 NO THIS IS NOT FROM GRADED ASSIGNEMNT

Answer 1

In general, the compound interest formula is

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ P\to\text{initial amount} \\ r\to\text{ interest rate} \\ n\to\text{ number of times interest applied per time period} \\ t\to\text{ time (in time periods)} \end{gathered}`

Therefore, in our case,

`n=12,t=2,A=45000,r=60\%=0.6`

Thus,

`\begin{gathered} \Rightarrow45000=P(1+(0.6)/(12))^(12\cdot2) \\ \Rightarrow P=(45000)/((1+(0.6)/(12))^(12\cdot2)) \\ \Rightarrow P=(45000)/((1.05)^(24)) \end{gathered}`

a) Thus, the exact amount is 45000/(1.05)^24 dollars.

b) Rounding to two decimal places,

`\begin{gathered} \Rightarrow P=13953.05596\ldots \\ \Rightarrow P=13953.06 \end{gathered}`

The rounded answer is $13953.06