Bank interest on a minimum monthly balance

A fictional account pays 0.5% monthly interest on its minimum monthly balance. Its complete balance-change history is $1,200, then $800, then $1,100, unchanged between entries. Which balance sets this month’s interest?

This is the complete balance-change history, unchanged between entries. Interest is 0.5% per month on the minimum; a $5 monthly fee is then deducted. All balances shown are before both adjustments. Try middle balances of $600, $1,000, $1,100 and $1,500

Why does raising the middle balance above $1,100 stop increasing interest?

Separate interest, fees and the balance

Read the fictional account rule before choosing a balance. These examples use a monthly rate on the minimum monthly balance. Interest is a credit, fees are debits, and their combined change can be positive, zero or negative

1. 1Read the account rule This fictional account uses the minimum balance over the whole month. Other accounts may use different rules. The complete balance-change history includes the opening balance; balances are unchanged between entries
2. 2Use the stated monthly rate B is the minimum monthly balance in dollars; r is the monthly percentage number. Use the monthly percentage number as shown in the formula below, and do not divide a monthly rate by twelve \(\displaystyle I=B(r/100)\)
3. 3Include all fees F is the sum of listed fees, I is interest and N the signed net change, all in dollars. Interest and fees are applied after the displayed balances \(\displaystyle N=I-F\)
4. 4Interpret the result Positive N means a net credit; negative N means a net debit; zero means no net change. This change is not the closing balance itself

Opening

\(\displaystyle \$1{,}480\)

Next balance

\(\displaystyle \$1{,}325\)

Next balance

\(\displaystyle \$1{,}410\)

Closing

\(\displaystyle \$1{,}290\)

Find the minimum. This is the complete balance-change history, with no changes between entries

Compare every balance, including the closing balance

Minimum monthly balance

\(\displaystyle \$1{,}180\)

Monthly interest rate

\(\displaystyle 0.9\%\)

Calculate one month’s interest under the minimum-balance rule

Apply the monthly percentage directly to the minimum

Account fee

\(\displaystyle \$3.20\)

Transaction fees

\(\displaystyle \$1.75\)

Statement fee

\(\displaystyle \$0.80\)

Find the total fee debit for the month

Add every listed fee once

Monthly interest

\(\displaystyle \$6.08\)

Total monthly fees

\(\displaystyle \$9.50\)

Find the signed net change from interest and fees. Use positive for credit and negative for debit

Subtract fees from interest, keeping the sign

An account earns $5.00 interest and has $5.00 in fees. What is the net effect?

Closing balance before adjustments

\(\displaystyle \$1{,}330\)

Monthly interest

\(\displaystyle \$10.28\)

Total fees

\(\displaystyle \$9.20\)

The closing balance below is before the month-end adjustments. Find the balance after interest and fees are applied

Add the signed net change to the pre-adjustment closing balance

A student uses a minimum balance of $900, a monthly rate of 0.8% and fees of $6. Which line first breaks the stated model?

You only know balances on three selected dates. The account uses the minimum over the entire month. Is the smallest of those three observations enough to establish that minimum?

Investigate a rule and explain its limits

Model a fictional account with complete monthly balance changes of $1,400, $900 and $1,100, unchanged between entries. It pays 0.6% monthly on the minimum and charges $6 in monthly fees. Calculate interest, the signed net change and the adjusted closing balance. Your written reasoning needs human review

1. 1State timing and assumptions Balances are before interest and fees, both applied at month end. Identify the minimum rather than using the closing balance for interest
2. 2Explore a change First replace only the $900 balance with $1,000, then with $1,200. Predict and calculate each net change. Explain when the closing balance becomes the minimum and why further increases to that middle balance have no effect
3. 3Evaluate the evidence Explain what changes if the three records are only occasional observations. Identify what information is missing before using this model for a real account