Solved: **In this question, give all answers to two decimal places.** Bryan decides to... [IB Mathematics Applications & Interpretation (Math AI)]

Question

SLPaper 2

In this question, give all answers to two decimal places.

Bryan decides to purchase a new car with a price of €14 000, but cannot afford the full amount. The car dealership offers two options to finance a loan.

Finance option A:

A 6 year loan at a nominal annual interest rate of 14% compounded quarterly. No deposit required and repayments are made each quarter.

Finance option B:

A 6 year loan at a nominal annual interest rate of $r$ % compounded monthly. Terms of the loan require a 10% deposit and monthly repayments of €250.

State which option Bryan should choose. Justify your answer.

[2]

Verified

Solution

Method #1

Bryan should choose Option A A1
No deposit is required R1

Award R1 for stating that no deposit is required. Award A1 for the correct choice from that fact. Do not award R0A1.

Method #2

Bryan should choose Option B A1
Cost of Option A ( $6923.69) > cost of Option B (72 × 250 − 12600 =$ 5400) R1

Award R1 for a correct comparison of costs. Award A1 for the correct choice from that comparison. Do not award R0A1.

Find the amount to be borrowed for this option.

[2]

Verified

Solution

$0.9 \times 14000$ (= $14000 - 0.10 \times 14000$ ) M1
(€) 12600.00 A1

Find the annual interest rate, $r$ .

[3]

Verified

Solution

N = 72
PV = 12600
PMT = −250
FV = 0
P/Y = 12
C/Y = 12 M1A1

Award M1 for an attempt to use a financial app in their technology, award A1 for all entries correct. Accept PV = −12600 provided PMT = 250.

r = 12.56(%) A1

Bryan's car depreciates at an annual rate of 25% per year.

Find the value of Bryan's car six years after it is purchased.

[3]

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Solution

Method #1

$14000{\left( {1 - \frac{25}{100}} \right)^6}$ M1A1

M1 for substitution into compound interest formula, A1 for correct substitutions

= (€)2491.70 A1

Method #2

N = 6
I% = −25
PV = ±14000
P/Y = 1
C/Y = 1 A1M1

A1 for PV = ±14000, M1 for other entries correct

(€)2491.70 A1

Remember to include the currency symbol (€) in your final answer

Find the total amount paid for the car.

[2]

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Solution

4 × 6 × 871.82 M1
(€) 20923.68 A1

Find the interest paid on the loan.

[2]

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Solution

20923.68 − 14000 M1
(€) 6923.68 A1

Find the repayment made each quarter.

[3]

Verified

Solution

N = 24 M1
I% = 14
PV = −14000
FV = 0
P/Y = 4
C/Y = 4 A1

Award M1 for an attempt to use a financial app in their technology, award A1 for all entries correct. Accept PV = 14000.

(€)871.82 A1

**In this question, give all answers to two decimal places.**

Method #1

Method #2

Method #1

Method #2

Related topics

In this question, give all answers to two decimal places.