Question

Jason opened a savings account and deposited $700.00 as principal. The account earns 1% interest, compounded continuously. What is the balance after 1 year? Use the formula A = Pe^rt , 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

Jason will have approximately $707.04 in his account after 1 year, given a principal of $700 and an interest rate of 1% compounded continuously.

Step-by-step explanation:

Jason has opened a savings account with a principal of $700. This account earns interest compounded continuously at a rate of 1%. To calculate the balance after 1 year, we'll use the formula for continuous compounding, A = Pert, where P is the principal, e is the base of the natural logarithms, r is the interest rate as a decimal, and t is the time in years. In this case, P = $700, r = 0.01 (because 1% = 0.01), and t = 1.

Using these values, the account balance after 1 year is calculated as follows:

$700 * e(0.01 * 1)

Using a calculator, we find that e0.01 is approximately 1.01005. Therefore, the balance after 1 year is:

$700 * 1.01005 ≈ $707.04

Therefore, after 1 year, Jason's savings account balance, rounded to the nearest cent, would be approximately $707.04.

Answer 2

The balance after 1 is $7070.35.

Step-by-step explanation:

Compound continuous formula:

`A=Pe^(rt)`

A=The final balance

P=Principal

r= interest rate.

Jason deposited $700.00 as principal for 1 year at a rate 1%, compounded continuously.

Here A=$700.00, t= 1 year, r=1%=0.01

`A=7000e^(0.01 * 1)`

=$7070.35

The balance after 1 is $7070.35.