A=P(1+r/n)^nt
a) Suppose you deposit $3000 for 6 years at a 7% rate
To calculate the amount of money (A) you will have at the end of 6 years when depositing $3000 at a 7% interest rate compounded annually, we can use the formula:
A = P(1 + r/n)^(nt)
where:
A = the amount of money after time t
P = the principal amount (the initial deposit) = $3000
r = the annual interest rate in decimal form = 7% = 0.07
n = the number of times the interest is compounded per year = 1 (since it is compounded annually)
t = the number of years = 6
Now, we can substitute the given values into the formula:
A = 3000(1 + 0.07/1)^(1*6)
Simplifying further:
A = 3000(1 + 0.07)^6
Next, let's calculate the expression inside the parentheses:
(1 + 0.07)^6 = (1.07)^6 ≈ 1.5031
Substituting this value back into the formula:
A ≈ 3000 * 1.5031
Finally, we can calculate the value of A:
A ≈ $4,509.30
Therefore, after 6 years, with a $3000 deposit at a 7% interest rate compounded annually, you will have approximately $4,509.30.