The first bank offers an interest rate 3 % for the first year and 2 % for the next two years. We will use the exponential growth function.
A(t)= P(1+ r)^tThe function models the amount of money A(t) after t years, where P is the principal and r is the interest rate. For the first year, the interest rate is 3 %= 0.03. Let P be the amount of money we invested. Then the amount of money at the end of the year.
A(t)= P(1+ 0.03)^1 ⇔ A(t)=P(1.03)
For the second year, the principal is the amount of money at the end of the first year and the interest rate is 2 %=0.02 for two years.
A(t)= P(1.03)(1+0.02)^2 ⇕ A(t)=P(1.03)(1.02)^2
The total amount of money in the first bank after three years, A_1(3), is P(1.03)(1.02)^2.
b
The second bank offers an interest rate 2.49 % for three years. We will use the exponential growth function.
A(t)= P(1+ r)^t
The function models the amount of money A(t) after t years, where P is the principal and r is the interest rate. The interest rate is 2.49 %= 0.0249. We invest the same amount of money, P.
A(t)= P(1+ 0.0249)^3 ⇔ A(t)=P(1.0249)^3
The total amount of money in the second bank after three years, A_2(3), is P(1.0249)^3.
