Complete the balance using continuous compounding

Question

Use the formula for continuous compounding. To complete the balance in the account after one, five, and twenty years. Also find the APR for the account.

 A $12,000 deposit in an account with an APR of 3.75% the balance in the account after 1 year is___5 years___20 years___

Answer 1

The formula for continuous compounding is A = Pe^rt where A is the future amount of the investment, P is the principal invested, e is the mathematical constant e, which can be approximated as 2.71828, r is the annual interest rate and t is the time in years.

 

12,000*2.71828^.0375 = 12,458.54

 

You can approximate continuous compounding by compounding at small increments such as daily.

 

That should give you enough information to help you solve the 5-year and 20-year amounts:

 

5 years -- 14,474.76