At Mr. Neely bank, the interest rate offered to clients is 4.5% annually. If after three years at the bank he has earned $50 in interest, approximately how much money did he initially deposit? (Round your answer to the nearest dollar!)
P * (1.045^3 - 1) = 50
amount invested: $x
x(1.045)^3 - x = 50
x(1.045^3 - 1) = 50
x = 50 / (1.045^3 - 1) - ....
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount (including interest)
P is the principal amount (initial deposit)
r is the annual interest rate (as a decimal)
n is the number of times that interest is compounded per year
t is the time in years
We are given the annual interest rate of 4.5% (or 0.045 as a decimal), and the interest earned after three years, which is $50.
Let's use the formula and solve for P, the principal amount:
50 = P(1 + 0.045/1)^(1*3)
Simplifying the equation:
50 = P(1 + 0.045)^3
Next, we can find the value of (1 + 0.045)^3:
(1 + 0.045)^3 ≈ 1.140096125
Substituting this value back into the equation:
50 = P * 1.140096125
Now, divide both sides of the equation by 1.140096125 to solve for P:
P ≈ 50 / 1.140096125 ≈ 43.83064516
Rounding to the nearest dollar, the initial deposit is approximately $44.