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Question 1197649: A bank loan of $8000 is repaid in annual payments of $1000plus 10% interest on the unpaid balance.What is the total amount of interest paid?
Thank you.
Answer by ElectricPavlov(122)   (Show Source):
You can put this solution on YOUR website! To calculate the total amount of interest paid, we will break down the payments year by year and keep track of the unpaid balance and the interest accrued. The loan is structured such that an annual payment of $1000 is made, along with 10% interest on the unpaid balance at the start of each year.
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### Breakdown of Payments
1. **Initial Loan Amount**: $8000
2. **Annual Payment**: $1000 (plus 10% interest on the unpaid balance)
#### Year-by-Year Calculation
| Year | Beginning Balance | Interest (10%) | Payment | Ending Balance |
|------|-------------------|----------------|---------|----------------|
| 1 | $8000 | $800 | $1000 | $7800 |
| 2 | $7800 | $780 | $1000 | $7580 |
| 3 | $7580 | $758 | $1000 | $7338 |
| 4 | $7338 | $734 | $1000 | $7072 |
| 5 | $7072 | $707 | $1000 | $6779 |
| 6 | $6779 | $678 | $1000 | $6457 |
| 7 | $6457 | $646 | $1000 | $6103 |
| 8 | $6103 | $610 | $1000 | $5713 |
| 9 | $5713 | $571 | $1000 | $5284 |
| 10 | $5284 | $528 | $1000 | $4812 |
| 11 | $4812 | $481 | $1000 | $4293 |
| 12 | $4293 | $429 | $1000 | $3722 |
| 13 | $3722 | $372 | $1000 | $3094 |
| 14 | $3094 | $309 | $1000 | $2393 |
| 15 | $2393 | $239 | $1000 | $1616 |
| 16 | $1616 | $162 | $1000 | $778 |
| 17 | $778 | $78 | $856 | $0 |
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### Total Interest Paid
To find the total interest paid, sum up all the interest amounts:
\[
800 + 780 + 758 + 734 + 707 + 678 + 646 + 610 + 571 + 528 + 481 + 429 + 372 + 309 + 239 + 162 + 78 = 8002
\]
### Final Answer
The total amount of interest paid is **$8002**.
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