Question

Mario deposits $1000 into a compound interest account. The interest rate for the account is 5%. Use a graphing calculator to estimate the number of years it will take for the account balance to double the original amount.

Answer 1

To estimate the number of years it will take for the account balance to double, use the formula for compound interest and solve for the number of years.

Step-by-step explanation:

To estimate the number of years it will take for the account balance to double, we can use the formula for compound interest:

A = P(1+r/n)^(nt),

where A is the final account balance, P is the initial deposit, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = $1000, r = 5% = 0.05, and we need to find t.

Let's set A = 2P and solve for t:

2P = P(1+0.05/n)^(nt)

Cancelling out P, we get:

2 = (1+0.05/n)^(nt)

Using a graphing calculator, we can plot the left side of the equation (y = 2) and the right side of the equation (y = (1+0.05/n)^(nt)) and find the value of t when the two graphs intersect. This will give us an estimate for the number of years it will take for the account balance to double.