Final answer:
To find how long it will take for the total amount to reach $6,500, we can use the formula for simple interest. In this case, it will take approximately 8.93 years (or 8 years and 11 months) for the total amount to reach $6,500.
Step-by-step explanation:
To calculate how long it will take for the total amount in the account to reach $6,500, we can use the formula for simple interest: A = P(1 + rt), where A is the total amount, P is the principal amount, r is the interest rate, and t is the time in years. In this case, we have A = $6,500, P = $4,000, and r = 7%. We can solve for t:
$6,500 = $4,000(1 + 0.07t)
Dividing both sides of the equation by $4,000, we get:
1.625 = 1 + 0.07t
Subtracting 1 from both sides of the equation, we get:
0.625 = 0.07t
Dividing both sides of the equation by 0.07, we get:
t = 0.625 / 0.07
Therefore, it will take approximately 8.93 years (or 8 years and 11 months) for the total amount to reach $6,500.