Chen borrows $17000 for his holiday. This loan has an interest rate of 9.5% per annum and monthly repayments of $427 for a period of 4 years. Calculate the monthly interest rate as a decimal to 8 places.
A Reducible Loan is a loan where the interest is paid on the balance owing, or the remaining amount of the loan that is yet to be paid.
First, summarise the data given in the problem.
Principal (P) =$17000
Monthly Repayment =$427
Loan Duration =4 years
Interest (I) =9.5% per annum
Solve for the monthly interest rate by dividing I by 12.
9.5%÷12
=
9.5100÷12
Convert from percentage to decimal
=
0.007916666.6
Use the calculator to solve
=
0.00791667
Round off to 8 decimal places
0.00791667
Question 2 of 4
2. Question
Chen borrows $17000 for his holiday. This loan has an interest rate of 9.5% per annum and monthly repayments of $427 for a period of 4 years. The table below sets out his monthly repayment schedule for the first three months. Find the missing values A,B and C.
A Reducible Loan is a loan where the interest is paid on the balance owing, or the remaining amount of the loan that is yet to be paid.
Reducible Loan Table
Month
Principal (P)
Interest (I)
P and I
P+I-R
Remaining loan amount
Interest amount for the month
Principal + Interest
Principal + Interest - Repayment
Finding A
First, summarise the data given in the problem.
Principal (P) =$17000
Monthly Repayment =$427
Loan Duration =4 years
Interest (I) =9.5% per annum
Interest per month =0.00791667 (from last question)
In the table, A is the interest paid in the 2nd month.
To solve this, multiply the monthly interest rate to that month’s principal value.
Interest per month =0.00791667 (from last question)
Principal amount for 2nd month =16707.58
A
=
0.00791667×16707.58
A
=
$132.27
Month
Principal (P)
Interest (I)
P and I
P+I-R
1
17000
134.58
17134.58
16707.58
2
16707.58
132.27
16839.85
16412.85
3
16412.85
129.94
16542.79
B
Sum
C
Finding B
From the table, B is the P+I-R in the 3rd month.
To solve this, simply subtract the monthly repayment from the P and I for that month.
Monthly Repayment =$427
P and I (3rd month) =$16542.79
B
=
$16542.79-$427
B
=
$16115.79
Month
Principal (P)
Interest (I)
P and I
P+I-R
1
17000
134.58
17134.58
16707.58
2
16707.58
132.27
16839.85
16412.85
3
16412.85
129.94
16542.79
16115.79
Sum
C
Finding C
From the table, C is the sum of the interest paid in the first three months.
I (1st month) =$134.58
I (2nd month) =$132.27
I (3rd month) =$129.94
C
=
134.58+132.27+129.94
C
=
$396.79
Month
Principal (P)
Interest (I)
P and I
P+I-R
1
17000
134.58
17134.58
16707.58
2
16707.58
132.27
16839.85
16412.85
3
16412.85
129.94
16542.79
16115.79
Sum
396.79
A=$132.27
B=$16115.79
C=$396.79
Question 3 of 4
3. Question
Constance borrows $22000 from the bank to buy office equipment. The interest on the loan is charged at 5.9% per annum which she has to pay at the end of every month. She made repayments of $516 every month for a period of 4 years. The table below sets out her monthly repayment schedule for the first four months. Find the missing values x,y and z.
A Reducible Loan is a loan where the interest is paid on the balance owing, or the remaining amount of the loan that is yet to be paid.
Reducible Loan Table
Month
Principal (P)
Interest (I)
P and I
P+I-R
Remaining loan amount
Interest amount for the month
Principal + Interest
Principal + Interest - Repayment
Finding x
First, summarise the data given in the problem.
Principal (P) =$22000
Interest (I) =5.9% per annum
Loan Duration =4 years
Monthly Repayment =$516
In the table, x is the principal amount in the 1st month.
Since it has just been the start of the loan, that means:
x=$22000
Month
Principal
Interest
P and I
P+I-R
1
22000
108.17
22108.17
21592.17
2
21592.17
y
21698.33
21182.33
3
21182.33
104.15
21286.48
20770.48
4
20770.48
102.12
20872.60
z
Finding y
From the table, y is the interest amount in the 2nd month.
Solve for the monthly interest rate by dividing I by 12.
Interest (I) =5.9% per annum/year
5.9%÷12
=
5.9100÷12
Convert from percentage to decimal
=
0.059÷12
Move decimal 2 places to the left
=
0.0049166667
Multiply the monthly interest rate to the 2nd month’s principal amount
2nd month Principal Amount =$21592.17
y
=
0.0049166667×21592.17
=
$106.16
Month
Principal
Interest
P and I
P+I-R
1
22000
108.17
22108.17
21592.17
2
21592.17
106.16
21698.33
21182.33
3
21182.33
104.15
21286.48
20770.48
4
20770.48
102.12
20872.60
z
Finding z
From the table, z is the P+I-R for the 4th month.
P and I (4th month) =$20872.60
R (Monthly Repayment) =$516
P+I-R
=
20872.60-516
z
=
$20356.60
Month
Principal
Interest
P and I
P+I-R
1
22000
108.17
22108.17
21592.17
2
21592.17
106.16
21698.33
21182.33
3
21182.33
104.15
21286.48
20770.48
4
20770.48
102.12
20872.60
20356.60
x=$22000
y=$106.16
z=$20356.60
Question 4 of 4
4. Question
Constance borrows $22000 from the bank to buy office equipment. The interest on the loan is charged at 5.9% per annum which she has to pay at the end of every month. She made repayments of $516 every month for a period of 4 years. What is the total amount that Constance paid over the loan period?