On 1 July 2010, David bought a tractor

Nthabi Irene

Nthabi Irene

Answered question

2022-09-14

On 1 July 2010, David bought a tractor for R2000000. On that day, he paid a deposit of 25% of the purchase price and the bank granted him a loan at an interest rate of 9.5% per annum, compounded quarterly, to pay of the balance of the purchase price. David agreed to pay quarterly installments of R58000, starting on 1 January 2011. How many installments are required to pay off the loan?

Answer & Explanation

madeleinejames20

madeleinejames20

Skilled2023-06-04Added 165 answers

Calculate the deposit David paid on 1 July 2010.
The deposit is 25% of the purchase price, which is R2000000.
25% of R2000000=25100×R2000000=R500000
So, David paid a deposit of R500000.
Determine the balance of the purchase price after the deposit.
The balance is the remaining amount to be paid after the deposit.
Balance=Purchase priceDeposit
Balance=R2000000R500000=R1500000
The balance remaining after the deposit is R1500000.
Calculate the interest on the balance.
The interest rate is 9.5% per annum, compounded quarterly. To calculate the interest, we need to determine the number of quarters.
The loan period is from 1 July 2010 to 1 January 2011, which is a duration of 6 months. Since interest is compounded quarterly, we have 2 quarters.
Let's calculate the interest using the formula for compound interest:
A=P(1+rn)nt
where:
A = final amount (balance + interest)
P = principal amount (balance)
r = annual interest rate (in decimal form)
n = number of compounding periods per year
t = number of years
Plugging in the values:
A=R1500000(1+0.0954)4×12
Simplifying the equation:
A=R1500000(1+0.02375)2
A=R1500000×1.023752
AR1555365.47
The amount after including interest for 6 months is approximately R1555365.47.
Determine the number of installments required.
Each installment is R58000, and we need to pay off the loan amount of R1555365.47.
Number of installments =Loan amountInstallment amount
Number of installments =R1555365.47R58000
Number of installments 26.86
Since we can't have a fraction of an installment, we round up to the nearest whole number.
Number of installments =27
Therefore, David will need 27 installments to pay off the loan.

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