Recursion and Financial Modelling

A loan of $28 000 is charged interest at the rate of 6.4% per annum, compounding monthly. It is repaid with regular monthly payments of $1200. The final payment on the loan, correct to the nearest cent, will be A $1125.41 B $1131.41 C $1175.20 D $1181.47 E $1200

$1 181.47

A loan of $28 000 is charged interest at the rate of 6.4% per annum, compounding monthly. It is repaid with regular monthly payments of $1200. Correct to the nearest cent, the value of the loan after 5 months is:

$22 690.33

Leasa borrows $150 000 to purchase a flat. She will pay interest at the rate of 6.25% per annum, compounding fortnightly and will make fortnightly payments so that the loan is fully repaid after 15 years. Leasa's fortnightly repayments will be closest to

$593

The balance of a reducing-balance loan after n monthly payments can be modelled by the recurrence relation V0 = 12 000, Vn+1 = 1.0125Vn - 1300 After five months, the balance of the loan is

$6104

Lars invests $500,000 at 5.5% per annum, compounding half yearly. He makes regular deposits of $500 per half year into the account. What is the value of his investment after 5 years?

$661 491.90

Lars invests $500,000 at 5.5% per annum, compounding monthly. He makes regular deposits of $500 per month into the account. What is the value of his investment after 5 years?

$692 292.30

Lars invests $500,000 at 5.5% per annum, compounding fortnightly. He makes regular deposits of $500 per month into the account. What is the value of his investment after 5 years?

$732 800.14

Lars invests $500,000 at 5.5% per annum, compounding weekly. He makes regular deposits of $500 per week into the account. What is the value of his investment after 5 years?

$807 711.92

The balance of an annuity investment after n monthly payments can be modelled by the recurrence relation V0 = 50 000, Vn+1 = 1.0105Vn - 800 This investment has annual interest rate of ___________% and monthly payments of $800

12.6%

The balance of a reducing-balance loan after n monthly payments can be modelled by the recurrence relation V0 = 12 000, Vn+1 = 1.0125Vn - 1300 This loan has annual interest rate _______ and monthly payments of $1300

15%

The recurrence relation below is used to model a financial situation. V0 = 86 000, Vn+1 = 1.009Vn - 774 The financial situation could be a perpetuity with principal $86 000 earning ___________% per annum interest, compounding quarterly, with quarterly payments of $774

3.6%

A compound interest investment of $5000 has regular additions paid each quarter. Interest for the first quarter is $53.13.The annual percentage interest rate on this loan is

4.25%

The recurrence relation below is used to model a financial situation. V0 = 24 000, Vn+1 = 1.0205Vn - 492 The financial situation could be an interest only loan of $24 000 at ___________% per annum interest, compounding quarterly with quarterly payments of $492

8.2 %

Huiqing invests her superannuation funds of $250 000 into an annuity. This investment earns interest at the rate of 5.8% per annum, compounding fortnightly. Huiqing will receive fortnightly payments so that her annuity lasts for 15 years. Huiqing's fortnightly payments will be closest to A $960 B $1426 C $1688 D $2083 E $2750

A $960

The balance of an annuity investment after n monthly payments can be modelled by the recurrence relation V0 = 50 000, Vn+1 = 1.0105Vn - 800 12 After five months, the balance of the investment is closest to A $46 000 B $48 596 C $48 681 D $52 679 E $85 360

B $48 596

Tamir borrows $140 000 and is charged 6.9% compound interest per annum, compounding monthly. Tamir would like to fully repay this loan over a period of 10 years. The monthly payment that Tamir would have to pay is closest to A $1263 B $1363 C $1618 D $4313 E $5580

C $1618

Carol invests $170 000 into an annuity which pays 7.2% compound interest per annum, compounding monthly. If Carol receives monthly payments of $2000, the number of months that the annuity will last is closest to A 85 B 97 C 119 D 270 E 351

C 119

A recurrence relation that generates the sequence 3, 5, 9, 17, 33, ... is A T0 = 2, Tn+1 = Tn + 2 B T0 = 2, Tn+1 = Tn − 2 C T0 = 2, Tn+1 = 2Tn − 1 D T0 = 2, Tn+1 = 2Tn E T0 = 2, Tn+1 = 2Tn + 2

C T0 = 2, Tn+1 = 2Tn − 1

A recurrence relation that generates the sequence 2, 7, 22, 67, 202, ... is A T0 = 2, Tn+1 = Tn + 5 B T0 = 2, Tn+1 = 2Tn + 1 C T0 = 2, Tn+1 = 3Tn + 1 D T0 = 2, Tn+1 = 3.5Tn E T0 = 2, Tn+1 = 4Tn - 1

C T0 = 2, Tn+1 = 3Tn + 1

Perpetuity

An annuity where the regular payments or withdrawals are the same as the interest earned. The value of a perpetuity remains constant

Annuity

An investment that earns compound interest and from which regular payments are made

Janet deposited $1200 into an investment fund every month for 20 years to save for her retirement. Throughout the 20-year period, the investment fund paid 5.35% per annum compound interest, compounding monthly. When she retired, Janet purchased an annuity that pays 4.5% per annum compounding monthly, from which she receives a monthly payment for 20 more years. The monthly payment that Janet receives, correct to the nearest cent, is A $1956.80 B $2946.56 C $3164.50 D $3249.78 E $3490.15

D $3249.78

Carol invests $170 000 into an annuity which pays 7.2% compound interest per annum, compounding monthly. Carol would like the investment to provide monthly payments for a period of five years. The monthly payment that Carol will receive is closest to A $577 B $1020 C $2450 D $3382 E $6923

D $3382

Tamir borrows $140 000 and is charged 6.9% compound interest per annum, compounding monthly. If Tamir paid monthly payments of $2000, the number of months it takes to fully repay the loan is closest to A 32 B 45 C 74 D 78 E 90

E 90