Question

You déposit $100 each month into an account earning 4% interest compounded monthly.a) How much will you have in the account in 25 years?

Answer 1

hello

to solve this problem, we would simply use the formula of compound interest

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=\text{compounded interest} \\ p=\text{ principal} \\ r=\text{rate} \\ n=\text{ number of times compounded} \\ t=\text{time} \end{gathered}`

from this, we can write out our data and then substitute it into the formula

`\begin{gathered} a=\text{ ?} \\ p=100 \\ r=4\text{ \%=0.04} \\ n=12 \\ t=25\text{ years} \end{gathered}`
`\begin{gathered} A=p(1+(r)/(n))^(nt) \\ A=100*(1+(0.04)/(12))^(12*25) \\ A=100*(1+0.003)^(300) \\ A=100*(1.003)^(300) \\ A=100*2.456 \\ A=245.6 \end{gathered}`

in 25 years, i will have the sum of $245.6 after compounding $100 monthly at 4% interest rate