Question

HELP NEEDED!!!

A savings account is started with an initial deposit of $500. The account earns 4.5% 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 $1200. Show your work.

Answer 1

a) The formula for compound interest is:

Total = starting amount x (1 + interest rate)^ number of years

b)

Using the given information you have:

1200 = 500 x (1+0.045)^x where x is the length of time you want to find.

1200 = 500 (1.045)^x

Divide both sides by 500:

2.4 = 1.045^x

Use natural logarithms:

ln(1.045^x) = ln(2.4)

Solve for x:

X = ln(2.4) / ln(1.045)

X = 19.889 years ( Round the answer as needed).