Question

Carl invested $10000 into a CD that compounds quarterly with an annual interest rate of 4.5%. Determine how much money Carl would have after 10 years. Round your answer to the nearest cent and just put numbers for your final answer (this means that you can avoid symbols like "$" in your final answer

Answer 1

15643.77

Step-by-step explanation

to solve this we need to use the formula

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ where: \\ P\text{ is the prinicipal \lparen initial amount\rparen} \\ r\text{ is the interest rate \lparen in decimals\rparen} \\ n=number\text{ of times interest is compoun in a unit of time t} \\ \text{t is the time} \end{gathered}`

so

Step 1

a)let

`\begin{gathered} P=\text{ 10000} \\ n=4 \\ r=4.5\text{ \%= }(4.5)/(100)=0.045 \\ t=10\text{ years} \end{gathered}`

b) now, replace in the formula

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=10000(1+(0.045)/(4))^(4*10) \\ A=10000(1+0.01125)^(40) \\ A=10000(1.01125)^(40) \\ A=10000(1.564) \\ A=15643.77 \end{gathered}`

therefore, the answer i

15643.77

I hope this helps you