Colton opened a savings account and deposited $300.00. The account earns 2% interest, compounded continuously. If he wants to use the money to buy a new bicycle in 1 year, how much will he be able to spend on the bike?

Question

Use the formula A=Pert, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (≈2.71828), r is the interest rate expressed as a decimal, and t is the time in years.
Round your answer to the nearest cent.

Answer 1

To find out how much Colton will have in his savings account after 1 year with continuous compounding interest, we can use the formula \( A = Pe^{rt} \).

Given:

• \( P = 300.00 \) (the principal amount)
• \( r = 0.02 \) (the interest rate as a decimal)
• \( t = 1 \) (the time in years)
• \( e \) is approximately 2.71828

Now, substitute the values into the formula:

\[ A = 300.00 \cdot e^{0.02 \cdot 1} \]

Calculate \( 0.02 \cdot 1 = 0.02 \).

Now, calculate \( e^{0.02} \):

\[ e^{0.02} \approx 1.020201 \]

Now substitute this value back into the formula:

\[ A \approx 300.00 \cdot 1.020201 \]

Calculating this:

\[ A \approx 306.0603 \]

Rounding this to the nearest cent, we get:

\[ A \approx 306.06 \]

Thus, Colton will be able to spend approximately $306.06 on the bicycle after 1 year.