SOLUTION: 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.

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.
---
### 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 |
---
### 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**.
RELATED QUESTIONS
A bank loan of $8000 is repaid in annual payments of $1000 plus 10% interest on the... (answered by Theo,MathTherapy,ikleyn)

1st question: If the sum of the first two terms of an arithmetic sequence equals the sum (answered by greenestamps)

21. Maybank will loan you RM7,500 for two years to buy a car. The loan must be repaid in... (answered by Boreal)

off with monthly payments where f is the finance charge on the Loan p is the number of... (answered by Theo)

A loan of 2400 dollars is to be paid in the following manner; 300 dollars will be paid at (answered by harpazo)

You borrowed $500 from your parents to buy a computer. The arrangements of the loan are... (answered by richwmiller)

On January 1, Mustafa borrows $1000 on a demand loan from his bank. Interest is paid at... (answered by Theo)

A loan of $ 12,000 is to be repaid within one year with level monthly payments, due at... (answered by Theo,ikleyn)

A ₱38,000 loan bears interest at 10% compounded semi-annually and is to be repaid in... (answered by proyaop,ikleyn)