One Christmas, alex took all the money he received as a gift and put it into a savings account. The account earned 5% interest and he left it in the bank for 4 years. if he earned %40 interest, what was the original principal
To find the original principal, we need to determine the amount after both years using the formula:
A = P(1 + r/n)^(nt)
Where:
A = Amount after time t
P = Principal amount
r = Annual interest rate (as a decimal)
n = Number of times that interest is compounded per year
t = Number of years
Let's plug in the given values to find the original principal:
A = P(1 + r/n)^(nt)
1.4P = P(1 + 0.05/1)^(1*4)
1.4P = P(1.05)^4
1.4P = 1.2155P
To find P, we divide both sides of the equation by 1.2155:
P = 1.4P / 1.2155
P = 1.15085P
Thus, the original principal was equal to $1.15085P.