Question

you deposit $8000 in a savings account that earns 4.3% annual interest compounded monthly. You also save $80 per month in a safe at home. write a function for the total amount of money saved C(t) =b (t)+h (t), where b (t) represents the balance of you savings account and h (t) represents the amount in your safe after t years. round any decimals to three places please.

Answer 1

$C(t)=8000(1.004)^{12t}+960t$

Our first function, b(t), is given by:

$\\b(t)=p(1+\frac{r}{12})^{12t} \\ \\b(t) = 8000(1+\frac{0.043}{12})^{12t} \\ \\=8000(1+0.004)^{12t} = 8000(1.004)^{12t}$

Our second function, h(t), is given by:
h(t) = 80(12t) = 960t

Together, we have
C(t) = b(t) + h(t)
$C(t)=8000(1.004)^{12t}+960t$