A man borrowed RM 5000 from a bank on 1 january 2006. On the last day each month, compound interest at the rate of 1.2% per month on the amount he owned is added. The man repays the debt in 24 equal installments made on the first day of each month the first installment being paid on 1 Febuary 2006. Find the amount of each installment.
To solve this problem, we can break it down into smaller steps and calculations.
Step 1: Calculate the total amount owed after 24 installments.
- The man borrowed RM 5000 from the bank.
- The interest rate is 1.2% per month.
- The loan will be repaid in 24 equal installments.
- The first installment was paid on 1 February 2006.
To find the total amount owed after 24 installments, we need to calculate the accumulated compound interest on the original loan amount.
Step 2: Calculate the compound interest for each month.
- The compound interest formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (loan amount), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.
- In this case, the interest is compounded monthly, so n = 12 (12 months in a year).
- The interest rate is 1.2% per month, so r = 0.012.
- The loan was taken on 1 January 2006, and the repayments end on 1 January 2008 (24 installments over 2 years).
- Therefore, t = 2.
Step 3: Calculate the total amount owed.
- After 24 months, the accumulated compound interest on the original loan amount will be added to the loan amount.
- This will give us the total amount owed after 24 installments.
Now, let's calculate the compound interest for each month:
Month 1: February 2006
- Principal (P) = RM 5000
- Interest rate (r) = 0.012
- Number of compounding periods (n) = 12
- Time (t) = 2/12 = 1/6 (since there are 12 months in a year)
Using the compound interest formula, we can calculate the amount after 1 month:
A(1) = 5000(1 + 0.012/12)^(12*(1/6))
Month 2: March 2006
- Principal (P) = A(1) (amount after 1 month)
- Interest rate (r) = 0.012
- Number of compounding periods (n) = 12
- Time (t) = 1/6 - 1/12 = 1/12 (since there are 12 months in a year, and we have already completed 1 month)
Using the compound interest formula, we can calculate the amount after 2 months:
A(2) = A(1)(1 + 0.012/12)^(12*(1/12))
Repeat this process for each month until the 24th month.
Step 4: Calculate the amount of each installment.
- Divide the total amount owed after 24 installments by 24 to find the amount of each installment.
By following these steps, you can find the amount of each installment.