A farmer is buying a tractor for R 750 000. He can afford a 15% deposit and will finance the rest over 10…

Question

A farmer is buying a tractor for R 750 000. He can afford a 15% deposit and will finance the rest over 10 years at an annual interest rate of 8.6%, compounded monthly. Calculate the deposit amount and

ScanSolve AI Tutor · Accepted Answer

Here are the calculations for the deposit and monthly instalments:

1. Calculate the deposit amount.

Identify the cost of the tractor and the deposit percentage.
The tractor costs R 750 000.
The deposit is 15% of the tractor cost.
Calculate the deposit amount.
$\text{Deposit amount} = 15\% \times \text{R } 750\,000$ $\text{Deposit amount} = 0.15 \times 750\,000$ $\text{Deposit amount} = \text{R } 112\,500$
The deposit amount is $\boxed{\text{R } 112\,500}$ .

2. Determine his monthly instalments.
Calculate the loan amount.
The loan amount is the tractor cost minus the deposit.
$\text{Loan amount} = \text{R } 750\,000 - \text{R } 112\,500$ $\text{Loan amount} = \text{R } 637\,500$
Determine the monthly interest rate and total number of payments.
Annual interest rate ( $r$ ) = 8.6% = 0.086
Compounded monthly, so the monthly interest rate ( $i$ ) is:
$i = \frac{r}{12} = \frac{0.086}{12}$
Loan period = 10 years
Total number of payments ( $n$ ) = 10 years $\times$ 12 months/year = 120 months
Use the present value of an annuity formula to find the monthly instalment ( $x$ ).
The formula is:
$P = \frac{x[1 - (1 + i)^{-n}]}{i}$
Rearrange to solve for $x$ :
$x = \frac{P \cdot i}{1 - (1 + i)^{-n}}$
Substitute the values: $P = \text{R } 637\,500$ , $i = \frac{0.086}{12}$ , $n = 120$ .
$x = \frac{637\,500 \times \frac{0.086}{12}}{1 - \left(1 + \frac{0.086}{12}\right)^{-120}}$ $x = \frac{637\,500 \times 0.00716666666...}{1 - (1.00716666666...)^{-120}}$ $x = \frac{4562.5}{1 - 0.420697902...}$ $x = \frac{4562.5}{0.579302098...}$ $x \approx 7876.00000...$
Rounding to two decimal places for currency:
$x = \text{R } 7876.00$
His monthly instalments will be $\boxed{\text{R } 7876.00}$ .

A farmer is buying a tractor for R 750 000. He can afford a 15% deposit and will finance the rest over 10 years at an annual interest rate of 8.6%, compounded monthly. Calculate the deposit amount and

Step-by-step solution

Identify the cost of the tractor and the deposit percentage.

Calculate the deposit amount.

Calculate the loan amount.

Determine the monthly interest rate and total number of payments.

Use the present value of an annuity formula to find the monthly instalment ( $x$ ).

Still stuck on this one?

More Mathematics Questions

A farmer is buying a tractor for R 750 000. He can afford a 15% deposit and will finance the rest over 10 years at an annual interest rate of 8.6%, compounded monthly. Calculate the deposit amount and

Step-by-step solution

Identify the cost of the tractor and the deposit percentage.

Calculate the deposit amount.

Calculate the loan amount.

Determine the monthly interest rate and total number of payments.

Use the present value of an annuity formula to find the monthly instalment (xxx).

Still stuck on this one?

More Mathematics Questions

Use the present value of an annuity formula to find the monthly instalment ( $x$ ).