Question

Use the formula for continuous compounding to compute the balance in the account after​ 1, 5, and 20 years.​ Also, find the APY for the account.
A ​$6000 deposit in an account with an APR of 3.75
​%

Answer 1

Using continuous compounding, the APY is of 3.75% and the balances are given as follows:

• 1 year: $6,229.

• 5 years: $7,237.

• 20 years: $12,702.

What is the continuous compounding formula?

The amount of money earned in continuous compounding, after t years, is given by:

$A(t) = A(0)e^{rt}$

In which:

• A(0) is the initial amount.

• r is the interest rate, which is also the APY.

For this problem, the parameters are given as follows:

A(0) = 6000, r = 0.0375.

Hence the balances are given by:

• $A(1) = 6000e^{0.0375(1)} = 6,229$

• $A(5) = 6000e^{0.0375(5)} = 7,237$

• $A(20) = 6000e^{0.0375(20)} = 12,702$

More can be learned about continuous compounding at https://brainly.com/question/24722580

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