Question

A bank has a special promotion going on. If you sign up for an account now, you get 2 years of 12% annual interest rate compounded monthly, after which you get 8% annual interestrate compounded monthly for the rest of time. If you deposit $200 now, how much will you have after 4 years?I want answer and explanation.

Answer 1

The compound interest formula is

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A\text{ is the amount} \\ P\text{ is the principal} \\ r\text{ is the interest rate} \\ t\text{ is the time in years} \end{gathered}`

If you sign up for an account now, you get 2 years of 12% annual interest rate compounded monthly, i.e.

`\begin{gathered} t=2\text{ years } \\ R=12\% \\ r=(R)/(100)=(12)/(100)=0.12 \\ n=12\text{ \lparen compounded monthly\rparen} \\ P=\text{\$200} \end{gathered}`

The amount after the first two years is

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=200(1+(0.12)/(12))^(12*2) \\ A=200(1+0.01)^(24) \\ A=200(1.01)^(24) \\ A=\text{\$253.95} \end{gathered}`

The amount after the first two years is $253.95 (nearest cent)

For the rest of the time, i.e. the next 2 years,

Where

`\begin{gathered} P=\text{\$253.95} \\ R=8\% \\ r=(R)/(100)=(8)/(100)=0.08 \\ n=12\text{ \lparen compounded monthly\rparen} \\ t=2\text{ years} \end{gathered}`

The amount for after 4 years will be

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=253.95(1+(0.08)/(12))^(12*2) \\ A=\text{\$297.85 \lparen nearest cent\rparen} \end{gathered}`

Hence, the amount after 4 years is $297.85 (nearest cent)