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IB Maths AI HL Sl 1 7 Amortization and Annuities Questions

Practise using annuity models to calculate payments, present or accumulated value, loan balances and repayment periods, while checking compounding and currency.

Syllabus
First assessment 2021
Course
Mathematics: applications and interpretation HL
Level
HL

Exam points

  • Use an annuity model to calculate regular end-of-period payments, accumulated value, present value or interest.
  • Determine an outstanding loan balance or the number of periods needed to repay a loan or reach a target balance.
  • Analyse how payment timing, compounding interval, deposits, withdrawals or a final repayment changes the financial result.
  • Use technology or the stated financial model accurately, then check rounding, currency and the contextual interpretation.

IB Maths AI HL Sl 1 7 Amortization and Annuities Questions question 1

[Maximum number: 12]

Give your answers in parts (a), (d)(i), (e) and (f) to the nearest dollar.
Daisy invested 37000 Australian dollars (AUD) in a fixed deposit account with an annual interest rate of 6.4 % compounded quarterly.

Question (a)

(a)

Daisy is saving to purchase a new apartment. The price of the apartment is 200000 AUD.
Daisy makes an initial payment of 25 % and takes out a loan to pay the rest.

Write down the amount of the loan.

[ 1 ]

Question (b)

(b)

The loan is for 10 years, compounded monthly, with equal monthly payments of 1700 AUD made by Daisy at the end of each month.

For this loan, find

[ 5 ]

Question (i)

(i)

the amount of interest paid by Daisy.

[ 2 ]

Question (ii)

(ii)

the annual interest rate of the loan.

[ 3 ]

Question (c)

(c)

After 5 years of paying off this loan, Daisy decides to pay the remainder in one final payment.

Find the amount of Daisy's final payment.

[ 3 ]

Question (d)

(d)

Find how much money Daisy saved by making one final payment after 5 years.

[ 3 ]
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