Question

asmonet opened a savings account with $2000. The account earns 1.8% simple interest annually. After how many years will the balance of the account be $2100? Round to the nearest tenth, if necessary.
After about (blank) year(s), the balance of the account will be $2100.

Answer 1

To find out how many years it will take for Asmonet's savings account balance to grow from $2000 to $2100 with a simple interest rate of 1.8%, we can use the simple interest formula:

\[
A = P(1 + rt)
\]

where:
- \(A\) is the amount of money accumulated after n years, including interest.
- \(P\) is the principal amount (the initial amount).
- \(r\) is the annual interest rate (in decimal).
- \(t\) is the time the money is invested or borrowed for, in years.

Given:
- \(A = 2100\)
- \(P = 2000\)
- \(r = 1.8\% = 0.018\)

We need to determine \(t\). Plugging the values into the formula:

\[
2100 = 2000(1 + 0.018t)
\]

Now, let's solve for \(t\):

1. Divide both sides by 2000:

\[
\frac{2100}{2000} = 1 + 0.018t
\]

\[
1.05 = 1 + 0.018t
\]

2. Subtract 1 from both sides:

\[
1.05 - 1 = 0.018t
\]

\[
0.05 = 0.018t
\]

3. Divide both sides by 0.018:

\[
t = \frac{0.05}{0.018} \approx 2.7778
\]

Rounding to the nearest tenth gives:

\[
t \approx 2.8
\]

Thus, after about **2.8 years**, the balance of the account will be $2100.