Question

Please read each statement and do what it says please!

Answer 1

Given that an investment accout is opend with an initial deposit of $6500, and the account chosen compounds interest annually.

A) Equation to calculate the compunded interest.

The interest is expressed as

`\begin{gathered} \text{Interest = Final amount - principal/initial deposit} \\ \text{where} \\ A=P(1+(r)/(n))^(nt) \\ A\Rightarrow\text{final amount} \\ P\Rightarrow pr\text{incipal or initial deposit} \\ r\Rightarrow\text{interest rate} \\ n\Rightarrow number\text{ of times interest applied per }time\text{ period} \\ t\Rightarrow period \\ \text{thus, we have} \\ I=P(1+(r)/(n))^(nt)-P \\ \text{where} \\ I\text{ is the compounded interest} \end{gathered}`

B) Value of the account after 10 years, if interest is paid at 3.7%, if no other withdrawals or deposits are made.

This implies that

`\begin{gathered} t=10,\text{ n=1} \\ r=(3.7)/(100)=0.037 \\ \text{recall that} \\ P=6500 \end{gathered}`

thus,

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ =6500(1+(0.037)/(1))^(10(1)) \\ \Rightarrow A=9347.61723 \end{gathered}`

Thus, the value of the account after 10 years is

`\$9347.61723`

C) Interest earned if the account is left for 20 years.

In this case,

`t=20`

Thus, the interest is evaluated as

`\begin{gathered} I=P(1+(r)/(n))^(nt)-P \\ =6500(1+(0.037)/(1))^(20(1))-6500 \\ =13442.76121-6500 \\ I=\$6942.76121 \end{gathered}`

The interest when the account is left alone for 20 years is

`\$6942.76121`