Question

You have been making monthly deposits of $20 into a savings account with monthly compounding for 8 years, and you do not know what the account's apr is (so you cannot use the monthly deposits balance formula to compute the balance exactly). eventually you remember that the apy (not the apr) is 1.2%. use the upper bound/estimate for the balance (from the course video) to determine an upper bound for your account's balance.

Answer 1

To estimate the upper bound of the savings account balance with a given APY of 1.2%, we assume each $20 monthly deposit earns interest for 8 years. We calculate an upper bound estimate by applying the monthly equivalent of the annual interest rate to each $20 deposit for the full 96 months.

Step-by-step explanation:

Estimating the Upper Bound for a Savings Account Balance

Given the APY of 1.2% and monthly deposits of $20 for a period of 8 years, we want to estimate the upper bound of the savings account balance. Since the annual percentage yield is given, we can convert it to a monthly interest rate to approximate the compound interest earned over 8 years. However, we will use an upper bound estimation which assumes that each $20 deposit earns interest for the entire 8 years.

To calculate the upper bound, consider each $20 deposit as if it were invested at the APY of 1.2% for 8 years, compounded monthly:

• Number of periods (n) = 8 years × 12 months/year = 96
• Monthly rate (r) from APY = (1 + 0.012)^(1/12) - 1
• Total deposits = $20 × 12 months/year × 8 years = $1920

Upper bound estimate = $20 × (1 + r)^96 for every deposit made. Summing this up for every month gives us the total balance.

To compute the actual upper bound, we would iterate through each $20 deposit from month 1 to month 96 and apply this formula, then sum all the results.