Zandile is about to purchase a car for R191 810,00 on terms from a car dealer. The terms
are R23 235 deposit and the rest paid in equal quarterly payments of R13 292,48 at the end
of each quarter for four years. The interest rate is 11,5% per year, compounded quarterly.
Considering the amortisation schedule, the principal repaid during the third quarter of the
first year, is equal to? [1] R2 487,37. [2] R4 353,91. [3] R8 445,95. [4] R8 938,57.
Answers
Answer:
Answer is [4] R8 938.57
Step-by-step explanation:
Given;
Car cost = R191 810.00
Deposit = R23 235
Quarterly Payments = R13 292.48
Annual Interest Rate = 11.5%
Compound Period = quarterly
Amortization Schedule;
Payment Due = Principal + Compound Interest
Hence required;
3rd Quarter Principal = Quarterly Payment – 3rd Quarter Compound Interest
Compound Interest Total amount of Principal and Interest in future (or Future Value) less Principal amount at present (or Present Value). It is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one.
= [P (1 + r/n)^nt] – P
= P [((1 + r/n)^nt)-1]
Where; P = initial principal amount, r= interest rate (11.5%), n= number of times applied per time period (4 times in a year), t = number of time periods elapsed (quarter = ¼).
Compound Interest = P[((1 + 11.5%/4)4/4)-1] = 2.875%*P
Calculate Initial Loan Balance;
Loan Balance = Car cost- Deposit = R191 810.00- R23 235 = R168 575.00
1st Quarter:
Initial Loan Balance = initial principal amount (P) = R168 575.00
1st Quarter Principal Repaid = Quarterly Payment – 1st Compound Interest
= R13 292.48– 2.875%* R168 575.00 = R8 445.95
2nd Quarter:
1st Loan Balance = Initial Loan Balance - 1st Quarter Principal Repaid
= R168 575.00 - R8 445.95= R160 129.05
2nd Quarter Principal Repaid = Quarterly Payment – 2ndCompound Interest
= R13 292.48– 2.875%* R160 129.05= R8 688.77
3rd Quarter:
2nd Loan Balance = 1st Loan Balance – 2nd Quarter Principal Repaid
= R160 129.05- R8 688.77= R151 440.28
3rd Quarter Principal Repaid = Quarterly Payment – 3rd Compound Interest
= R13 292.48– 2.875%* R151 440.28= R8 938.57
Given : Zandile is about to purchase a car for R191 810,00 on terms from a car dealer. R23 235 deposit . equal quarterly payments of R13 292,48
to find : the principal repaid during the third quarter of the first year,
Solution:
Zandile is about to purchase a car for 191 810.00
Deposites = 23235
Remaining amount to pay = 191810.00 - 23235
= 168575
quarterly payments of 13292.48
Interest for 1st Quarter = 168575 * (11.5) / 400 = 4,846.53
Principle paid in 1st Quarter = 13 292.48 - 4846.53
= 8445.95
Remaining principle = 168575 - 8445.95
= 160129.05
Interest for 2nd Quarter = 160129.05 * (11.5) / 400 = 4603.71
Principle paid in 2nd Quarter = 13292.48 - 4603.71
= 8688.77
Remaining principle = 160129.05 - 8688.77
= 151440.28
Interest for 3rd Quarter = 151440.28 * (11.5) / 400 = 4353.9
Principle paid in 3rd Quarter = 13292.48 - 4353.9
= 8938.57
principal repaid during the third quarter of the first year, = R8938.75
option is [4] R8 938,57
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