Question

3. A savings account is started with an initial deposit of $3000. The account earns 9% interest compounded annually.

(a) Write an equation to represent the amount of money in the account as a function of time in years.
(b) Find the amount of time it takes for the account balance to reach 1 million. Show your work.
Note: 1 million is a 1 with 6 zeros. Note2: you must use log functions to solve.

Answer 1

See below

Explanation:

Given

• Deposit = $3000
• Interest rate = 9% compounded
• Number of years = t
• Number of compounds = 1 per year

Solution

(a) the equation

• f(t) = 3000*(1.09)^t

(b) If f(t) = 1000000

• 1000000 = 3000*(1.09)^t
• (1.09)^t = 1000000/3000
• (1.09)^t = 333.3333
• log (1.09)^t = log 333.3333
• t log 1.09 = 2.5229
• 0.03742t = 2.5229
• t = 2.5229/0.03742
• t = 67.4 ≈ 68 years