Week 3


In this week we learn about the effective interest rate, the annuity due and explore mortgage type questions. 

The Essentials

Which is the right annuity formula? 
What is a loan? 

Question 1

An interest rate of 10% p.a. compounding quarterly represents and effective interest rate of:

a. 10.18% p.a.
b. 10.25% p.a.
c. 10.38% p.a. 
d. 10.50% p.a.

Question 2

Five years ago Chris entered into a loan agreement with Bangkok Bank to borrow $200,000 and repay the loan over 20 years through equal monthly instalments. If the interest rate was fixed at 8% p.a. for the entire term of the loan, what is the amount of each monthly instalment? 

a. $1,333
b. $16,667
c. $833
d. $1,673

Question 3

Frank Lewis has a 30-year, $500,000 mortgage with Westpac Bank at a nominal interest rate of 8% p.a. and monthly compounding. Which of the following statements regarding his mortgage is most correct?

a. The monthly payments will decline over time.

b. The proportion of the monthly payment which represents interest will be lower for the last payment than for the first payment on the loan.

c. The total dollar amount of principal being paid off each month gets larger as the loan approaches maturity.

d. Statements B and C are correct.

Question 4

You bought a painting 10 years ago as an investment and you paid $85,000 for it. If you sold it for $484,050 what was your annual (compounded) return on the investment?

a. 47%
b. 4.7%
c. 12.8%
d. 19%

Question 5

Assuming an interest rate of 10% p.a., what is the amount of money a person must be given now to make them indifferent to receiving that sum or a stream of five annual payments of $50 each, where the first payment is received immediately:

a. $208
b. $190
c. $305
d. $232

Question 6

A bank offers an interest rate of 6% p.a. compounding semi-annually. How much would the future sum be if you made six semi-annual deposits of $50 each and the last deposit earned interest for one period?

a. $185
b. $333
c. $271
d. $365

Question 7

Joanne borrows $20,000 from HSBC Bank to buy a car. The loan involves equal annual repayments over 20 years and r = 10% p.a.

a. How much are Joanne’s annual repayments?

b. What is the value of the interest element of the 14th repayment?

c. How much is needed to pay off the loan at the time of the 16th repayment assuming the 16th repayment has not been made?

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