2021 ACJC Promo Q12
Mrs Tan plans to start a business which requires a start-up capital of $\$700,000$. She decided to first save $\$200,000$ by depositing money every month into a savings plan. For the remaining $\$500,000$, she intends to take a loan from a finance company.
She deposited $\$3000$ into the savings plan in the first month and on the first day of each subsequent month, she deposited $\$100$ more than the previous month. Mrs Tan will continue depositing money into the savings plan until the total amount in her savings plan reaches $\$200,000$. It is given that this savings plan pays no interest.
(i)
Find the month in which Mrs Tan’s monthly deposit will exceed $\$6550$.
[2]
(ii)
Find the number of months that it will take for Mrs Tan to save $\$200,000$ and hence find the amount that she would have deposited in the last month.
[4]
After Mrs Tan has saved $\$200,000$, she took a loan of $\$500,000$ from a finance company. To repay the loan from the finance company, Mrs Tan would have to pay a monthly payment of $\$x$ at the beginning of each month, starting from the first month. An interest of $0.3\%$ per month will be charged on the outstanding loan amount at the end of the month.
(iii)
Show that the outstanding amount at the end of ${{n}^{\text{th}}}$ month, after the interest has been charged, is $A\left( {{1.003}^{n}} \right)-Bx\left( {{1.003}^{n}}-1 \right)$, where $A$ and $B$ are exact constants to be determined.
[3]
(iv)
Find the amount of $\$x$, to $2$ decimal places, if Mrs Tan wants to fully repay her loan in $8$ years.
[2]
(v)
Using the value of $x$ found in part (iv), calculate the total interest that the finance company will earn from Mrs Tan at the end of $8$ years.
[2]
Suggested Video Solutions
Share with your friends!
Continue reading
5 Exam Preparation Tips: How We Help Students Excel in Exams
In the ever-evolving landscape of education, where academic success is often measured by performance in exams, the need for effective test preparation has never been more critical. Students face a
List MF 27
What is the MF 27? The MF 27, set to replace the MF 26 from 2025, is a comprehensive formula sheet developed by the Ministry of Education Singapore in collaboration
Panic No More: What To Do The Day Before An Exam?
As you approach the final hours before your exam, remember that a balanced approach is key. A light review can keep the information fresh in your mind, while preparing your