Question

If you invest this money ($7,185.51 ) in an account that compounds monthly with an APR of 2.5%, how much will you have saved i) after 1 year? ii) after 3 years?

Answer 1

Step-by-step explanation:

The principal is given below as

`P=7185.81`

The APR is given below as

`r=2.5\%=(2.5)/(100)=0.025`

Concept:

To figure out the the compund interest, we will use the formula below

`A=P(1+(r)/(n))^(nt)`

For one year, we will have the amount be

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ n=12,t=1 \end{gathered}`

By substituting the values, we would have

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=7185.51(1+(0.025)/(12))^(1*12) \\ A=7,185.51(1+(0.025)/(12))^(12) \\ A=7367.22 \end{gathered}`

Hence,

The amount ave after 1 year will be

`A=7,367.22`

To calculate the amount for three years, we will have

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ n=12,t=3 \\ \end{gathered}`

By substituting the values, we will have

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=7185.51(1+(0.025)/(12))^(3*12) \\ A=7,185.51(1+(0.025)/(12))^(36) \\ A=7744.54 \end{gathered}`

Hence,

The amount ave after 3 years will be

`\begin{equation*} 7744.54 \end{equation*}`