Difference between compounded daily or monthly?

Answer 1

Compound interest is interest that is paid on both the original principal balance and interest earned. For example, a $100 savings account with a 5% rate of interest compounded annually would have a balance of $105 at the end of year one. At the end of year two the account would earn interest income on the entire account balance of $105 and the interest payment would amount to $5.25 at which point the saver would have an account balance of $110.25. The extra 25 cents of income in year two represents interest on the previous year's interest.

Savings can be compounded on different dates including annual, monthly, daily, or continuously. The compounding date represents the date that the savings account balance is updated.

The difference between daily or monthly compounding does not result in materially different account balances at the end of the compounding period. For example, a $10,000 savings account compounded at 5% monthly would be worth $44,677 at the end of 30 years compared to an account balance of $44,812 when compounded daily.

Answer 2

Compounded daily means interest is calculated and added to the account balance every day, resulting in slightly higher overall returns compared to compounding monthly, where interest is calculated once at the end of each month. This difference is due to the more frequent compounding events in daily compounding.

Answer 3

One year from now, the Alfonso plan to renovate his basement. One company quoted $30 000 for the job.

a) Alfonso’s savings account pays 2.95% per year, compounded monthly. How much does he need to save each month to have $30000 in two years? Use the TVM Advanced Calculator. (4 points)

b) Calculate the monthly payment for a three-year personal loan of $30000 at 6.9% per year, compounded monthly. Use the TVM Advanced Calculator. (4 points)

c) How much money would Alfonso save by paying $30000 cash for the renovations instead of taking the