Brett takes out a personal loan of $36 000 to buy a boat. The terms of his loan specify monthly repayments of $595, with 8% per annum interest calculated monthly.Find the amount still owing after three months. (the dollar sign is not required)简答题
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Question

Brett takes out a personal loan of $36 000 to buy a boat. The terms of his loan specify monthly repayments of $595, with 8% per annum interest calculated monthly.Find the amount still owing after three months. (the dollar sign is not required)简答题

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BlackTom AI · Accepted Answer

Monthly interest rate = 8%/12 = 0.08/12 = 0.006666666666666667 (which is 1/150). Interest is charged each month on the outstanding balance, then the monthly repayment is deducted.

1) Relevant knowledge points
- Convert annual nominal rate to monthly rate by dividing by 12.
- Each month: new balance = previous balance × (1 + r) − payment.
- Round final answer to cents.

2) Step-by-step computation (month-by-month)
Starting balance L0 = 36,000, monthly payment P = 595, monthly rate r = 1/150 ≈ 0.0066666667.

Month 1:
- Interest = 36,000 × r = 36,000 × 0.0066666667 = 240.00
- Balance before payment = 36,000 + 240 = 36,240.00
- After payment: L1 = 36,240.00 − 595 = 35,645.00

Month 2:
- Interest = 35,645.00 × r = 35,645 ÷ 150 = 237.6333333
- Balance before payment = 35,645.00 + 237.6333333 = 35,882.6333333
- After payment: L2 = 35,882.6333333 − 595 = 35,287.6333333

Month 3:
- Interest = 35,287.6333333 × r = 35,287.6333333 ÷ 150 = 235.2508888889
- Balance before payment = 35,287.6333333 + 235.2508888889 = 35,522.8842222222
- After payment: L3 = 35,522.8842222222 − 595 = 34,927.8842222222

Rounded to cents, the amount still owing after three months is 34,927.88.

3) Alternative check (formula)
Outstanding after n payments: L_n = L0(1+r)^n − P[( (1+r)^n − 1)/r]. Using r = 1/150 and n = 3 gives the same result 34,927.884222... → 34,927.88.

4) Why this is correct
This method correctly applies monthly compounding interest and the scheduled payment each month. Iterating month-by-month or using the closed-form formula yields identical balances.

5) Other options
Not applicable (short-answer question). No alternate choice matches the computed balance.

Conclusion: The amount still owing after three months is 34,927.88, matching the provided answer.

Brett takes out a personal loan of $36 000 to buy a boat. The terms of his loan specify monthly repayments of $595, with 8% per annum interest calculated monthly.Find the amount still owing after three months. (the dollar sign is not required)简答题

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