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 ​$13,000 deposit in an account with an APR of 4.5​%.

Answer 1

• 1 yr: $13,598.36
• 5 yr: $16280.20
• 20 yr: $31,974.84
• APY: 4.6%

Explanation:

The formula for continuous compounding for t years at an APR of r is ...

A = Pe^(rt)

Then for 1 year, the amount for P=13,000 and r=.045 is ...

A = $13,000e^(.045) = $13,598.36

For 5 years, the amount is ...

A = $13,000e^(.045·5) = $16,280.20

For 20 years, the amount is ...

A = $13,000e^(.045·20) = $31,974.84

__

The multiplier for 1 year is ...

e^.045 ≈ 1.04602786 = 1 + APY

This represents an APY of 4.603%.