Math / Algebra

QuestionBookwork code: 3 H allowed
The formula below can be used to calculate monthly mortgage repayments.
Archie borrows $£ 228,000$ for his mortgage. The monthly interest rate is $0.18 \%$ and he must make a repayment every month for the next 25 years.
Use the formula to calculate Archie's monthly mortgage repayment. Give your answer to the nearest $£ 1$ . $m=\frac{0.01 r b}{1-(1+0.01 r)^{-n}}$ $m$ is the monthly mortgage repayment ( $£$ ) $r$ is the monthly interest rate (\%) $b$ is the amount borrowed ( $£$ ) $n$ is the number of monthly repayments Zoom

Studdy Solution

STEP 1

1. Archie borrows £228,000 for his mortgage.
2. The monthly interest rate is 0.18%.
3. Archie must make a repayment every month for the next 25 years.
4. We need to calculate the monthly mortgage repayment using the given formula.
5. The formula provided is: $ m = \frac{0.01 r b}{1 - (1 + 0.01 r)^{-n}} \]
6. $ m $ is the monthly mortgage repayment in £.
7. $ r $ is the monthly interest rate in %.
8. $ b $ is the amount borrowed in £.
9. $ n $ is the number of monthly repayments.

STEP 2

1. Identify and assign values to the variables.
2. Substitute the values into the formula.
3. Calculate the expression in the denominator.
4. Calculate the expression in the numerator.
5. Divide the numerator by the denominator to find $m$ .
6. Round the result to the nearest £1.

STEP 3

Identify and assign values to the variables.
- $r = 0.18$ - $b = 228,000$ - $n = 25 \times 12 = 300$

STEP 4

Substitute the values into the formula.
$m = \frac{0.01 \times 0.18 \times 228,000}{1 - (1 + 0.01 \times 0.18)^{-300}}$

STEP 5

Calculate the expression in the denominator.
First, calculate $1 + 0.01 \times 0.18$ :
$1 + 0.01 \times 0.18 = 1.0018$
Then calculate $(1.0018)^{-300}$ :
$(1.0018)^{-300} \approx 0.60577$
Now calculate the entire denominator:
$1 - 0.60577 = 0.39423$

STEP 6

Calculate the expression in the numerator.
$0.01 \times 0.18 \times 228,000 = 410.4$

STEP 7

Divide the numerator by the denominator to find $m$ .
$m = \frac{410.4}{0.39423} \approx 1041.12$

STEP 8

Round the result to the nearest £1.
The monthly mortgage repayment is approximately:
$m = \boxed{1041}$

Was this helpful?

Studdy Solution

STEP 1

STEP 2

1. Identify and assign values to the variables.
2. Substitute the values into the formula.
3. Calculate the expression in the denominator.
4. Calculate the expression in the numerator.
5. Divide the numerator by the denominator to find $m$ .
6. Round the result to the nearest £1.

STEP 3

Identify and assign values to the variables.
- $r = 0.18$ - $b = 228,000$ - $n = 25 \times 12 = 300$

STEP 4

Substitute the values into the formula.
$m = \frac{0.01 \times 0.18 \times 228,000}{1 - (1 + 0.01 \times 0.18)^{-300}}$

STEP 5

Calculate the expression in the denominator.
First, calculate $1 + 0.01 \times 0.18$ :
$1 + 0.01 \times 0.18 = 1.0018$
Then calculate $(1.0018)^{-300}$ :
$(1.0018)^{-300} \approx 0.60577$
Now calculate the entire denominator:
$1 - 0.60577 = 0.39423$

STEP 6

Calculate the expression in the numerator.
$0.01 \times 0.18 \times 228,000 = 410.4$

STEP 7

Divide the numerator by the denominator to find $m$ .
$m = \frac{410.4}{0.39423} \approx 1041.12$

STEP 8

Round the result to the nearest £1.
The monthly mortgage repayment is approximately:
$m = \boxed{1041}$

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

STEP 2

1. Identify and assign values to the variables.2. Substitute the values into the formula.3. Calculate the expression in the denominator.4. Calculate the expression in the numerator.5. Divide the numerator by the denominator to find m m m.6. Round the result to the nearest £1.

STEP 3

Identify and assign values to the variables.- r=0.18 r = 0.18 r=0.18 - b=228,000 b = 228,000 b=228,000 - n=25×12=300 n = 25 \times 12 = 300 n=25×12=300

STEP 4

Substitute the values into the formula.m=0.01×0.18×228,0001−(1+0.01×0.18)−300m = \frac{0.01 \times 0.18 \times 228,000}{1 - (1 + 0.01 \times 0.18)^{-300}}m=1−(1+0.01×0.18)−3000.01×0.18×228,000​

STEP 5

STEP 6

Calculate the expression in the numerator.0.01×0.18×228,000=410.40.01 \times 0.18 \times 228,000 = 410.40.01×0.18×228,000=410.4

STEP 7

Divide the numerator by the denominator to find m m m.m=410.40.39423≈1041.12m = \frac{410.4}{0.39423} \approx 1041.12m=0.39423410.4​≈1041.12

STEP 8

Round the result to the nearest £1.The monthly mortgage repayment is approximately:m=1041m = \boxed{1041}m=1041​

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Identify and assign values to the variables.
2. Substitute the values into the formula.
3. Calculate the expression in the denominator.
4. Calculate the expression in the numerator.
5. Divide the numerator by the denominator to find $m$ .
6. Round the result to the nearest £1.

Identify and assign values to the variables.
- $r = 0.18$ - $b = 228,000$ - $n = 25 \times 12 = 300$

Substitute the values into the formula.
$m = \frac{0.01 \times 0.18 \times 228,000}{1 - (1 + 0.01 \times 0.18)^{-300}}$

Calculate the expression in the numerator.
$0.01 \times 0.18 \times 228,000 = 410.4$

Divide the numerator by the denominator to find $m$ .
$m = \frac{410.4}{0.39423} \approx 1041.12$

Round the result to the nearest £1.
The monthly mortgage repayment is approximately:
$m = \boxed{1041}$