Question

1.Suppose you will receive $14,000 in 10 months and another $8,000 in 22 months. If the discount rate is 5% per annum (compounding monthly) for the first 13 months, and 10% per annum (compounding monthly) for the next 9 months, what single amount received today would be equal to the two proposed payments? (answer to the nearest whole dollar; don’t include the $ sign or commas)

2. Jill wants to buy a car but needs to calculate how much she can afford to borrow. The maximum she can repay each month-end is $660 per month and the bank has indicated it will charge a fixed 6.9% p.a compounding monthly. If she takes a loan for 5 years how much can she afford to borrow? (Do not use the $ sign or commas; include cents e.g 24500.09)

3.Payments of $14,000 per quarter are deposited into a fund at the end of each quarter for 8 years. If interest is 6.6% p.a. compounding quarterly, the size of the fund at the end of 8 years will be (to nearest dollar but don’t include $ sign or commas):

4. Calculate the nominal interest p.a. compounded monthly that is equivalent to 3.7% p.a. compounded quarterly. (Correct your answer to the nearest 0.01%, e.g. 2.12%)

Answer 1

Solution 1:

Given:

Discounting rate for first 13 months (r) = 5% p.a. i.e., 0.416667% p.m

Discounting rate for next 9 months (r) = 10% p.a. i.e., 0.833333% p.m

Therefore,

Present Value Discounting Fatcor for 10th month = 1/1.004166710

= 0.959272

Present Value Discounting Fatcor for 22nd month = 1/1.0083333322

= 0.833123

• Single amount received today = (14000 * 0.959272) + (8000*0.833123)

= 20,095.

Solution 2:

Given:

Instalment = 660 p.m

Rate of interest compoounded monthly (r) = 6.9% i.e., 0.575% p.m.

Duration = 5years i.e., 60 months

Present Value Annuity Factor = 1/1.005751+1/1.005752..........1/1.0057560

=50.62252

Let the loan amount be x.

Therefore,

x/50.62252 = 660

x = 660*50.62252

x = 33410.87

She can afford to borrow $33,410.87.