You deposit $50 in an investment account that earns 7% annual interest compounded monthly. Write a function m that represents the balance (in dollars) of the investment account after t years. What is the balance after 3 years

To solve this problem, we can use the formula for compound interest:

[

A = P left(1 + frac{r}{n}right)^{nt}

]

Where:

– ( A ) is the amount of money accumulated after n years, including interest.

– ( P ) is the principal amount (the initial deposit or investment).

– ( r ) is the annual interest rate (decimal).

– ( n ) is the number of times that interest is compounded per year.

– ( t ) is the number of years the money is invested or borrowed.

For your case:

– ( P = 50 )

– ( r = 0.07 )

– ( n = 12 ) (since it is compounded monthly)

– ( t = 3 )

Substituting these values into the formula, we can write the function ( m(t) ):

[

m(t) = 50 left(1 + frac{0.07}{12}right)^{12t}

]

Now to find the balance after 3 years, we substitute ( t = 3 ):

[

m(3) = 50 left(1 + frac{0.07}{12}right)^{12 cdot 3}

]

[

m(3) = 50 left(1 + frac{0.07}{12}right)^{36}

]