Question: Question 50:
Peter took out a reducing balance loan where interest was calculated monthly. He planned to repay this loan fully, with eight equal monthly payments of $260.
Peter missed the fourth payment, but made a double payment of $520 in the fifth month. He then continued to make payments of $260 for the remaining three months.
Which graph could show the balance of the loan each month over the eight-month period?
A.
balance of
loan ($)
month
O 1 2 3 4 5 6 7 8
B.
balance of
loan ($)
month
O 1 2 3 4 5 6 7 8
C.
balance of
loan ($)
month
O 1 2 3 4 5 6 7 8
D.
balance of
loan ($)
month
O 1 2 3 4 5 6 7 8
E.
balance of
loan ($)
month
O 1 2 3 4 5 6 7 8
1. **Problem Statement:**
Peter has a reducing balance loan with monthly interest. He planned to repay it in 8 equal monthly payments of $260.
He missed the 4th payment but made a double payment of $520 in the 5th month, then paid $260 for the last 3 months.
We need to identify which graph correctly shows the loan balance over the 8 months.
2. **Understanding the loan balance behavior:**
- Normally, the loan balance decreases steadily each month by the payment amount minus interest.
- Missing the 4th payment means the balance does not reduce that month and may increase due to interest.
- The double payment in the 5th month will reduce the balance more sharply than usual.
- The remaining payments continue to reduce the balance steadily.
3. **Expected graph characteristics:**
- From month 0 to 3: balance decreases steadily.
- At month 4: balance does not decrease (missed payment), so balance may increase or stay the same.
- At month 5: balance drops sharply due to double payment.
- Months 6 to 8: balance decreases steadily again.
- The balance should reach near zero at month 8.
4. **Analyzing the options:**
- Graph A shows a decrease with a noticeable rise at month 5 after the missed 4th payment, then near zero at month 8.
- Graph B shows a smooth decrease with no rise at month 5, inconsistent with missed payment.
- Graph C shows steady early balance then sharp drop after month 5 but no rise at month 4.
- Graph D shows steady decline and steeper fall after month 5 but does not reach zero at month 8.
- Graph E shows balance zero at month 4 then increases again, which is impossible.
5. **Conclusion:**
Graph A best matches the expected behavior: a missed payment causing a rise or no decrease at month 4, a double payment causing a sharp drop at month 5, and balance near zero at month 8.
**Final answer:** Graph A