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?
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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
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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}
]