Credit cards intetest and payments

Question

Use a formula for continuous compounding to complete the balance in the account after 1, 5, and 20 years. Also find the APR for the account. A $12,000 deposit on an account with APR of 3.75%. The balance in the account after one year? After five years, and after 20 years?

Answer 1

The formula for continuous compounding is A = Pe^rt where A is the future amount, P is the invested Principal, r is the annual interest rate, t is the number of years and e is the mathematical constant that can be approximated by 2.718282.

 

For 1 year:

Amount = $12,000*e^.0375*1 = $12,458.54

 

For 5 years:$14,474.76

 

Continuous compounding can also be approximated by assuming compounding at very short intervals such as daily. For example, daily compounding for one year yields $12,458.52