Question

Problem 2.1 Calculate the present value of $10,000 due in 7 months using 6% p.a. simple interest.

                

Problem 2.2 A note with a maturity value of $100,000 was purchased 46 days before maturity for $99,218.63. Calculate the rate of simple interest p.a. used.

Problem 2.3 Calculate the present (discounted) value at 5% p.a. payable monthly of $1,000.

(a) due at the end 4 years,

(b) due at the end 6 years.

Problem 2.4 If j₄ = 5:8% calculate

(a) j₂,

(b) j₁₂.

Problem 2.5 A person has debts of $1,000 due on 1 July 2013 and $2,000 due on 1 January 2015. He wishes to pay $500 on 1 January 2014 and $X on 1 January 2016. Calculate X if interest is at 7% p.a. convertible half-yearly.

Problem 2.6 How long will it take for $2,000 to accumulate to $3,000 at 6%p.a. compounded continuously?

Problem 2.7 Investor A contributes $2,000 annually into a fund, the first deposit being on his 26th birthday and the last on his 65th birthday. How much will be in the fund immediately after the final deposit? Interest is at j₁ = 8%.

Problem 2.8 A company wishes to accumulate $100,000 by the end of 5 years. What level deposit should be made at the end of each quarter for 5 years if interest is at j₄ = 8%?

Problem 2.9 $500 is deposited at the end of each half-year for 10 years. Calculate the amount at the end of 10 years if interest is at j₂ = 5% for 3 years and j₂ = 7% thereafter.

Problem 2.10 Instead of paying $100 at the beginning of each month for 1 year, a person wants to make a single payment at the beginning of the year. Using j₁₂ = 6% how much should be paid at the beginning of the year?

Problem 2.11 A bond with face value of $100 and interest at j₂ = 7% is to be redeemed at par in 6 years.

(a) What is the size of the half-yearly interest payments?

(b) What is the size of the redemption payment?

(c) Draw a timeline showing the price paid (P), the interest payments and the redemption

payment.

(d) From your timeline, write down an equation of value, and hence calculate the price if

the yield to maturity is j₂ = 8%.

Answer 1

Problem 2.1 Calculate the present value of $10,000 due in 7 months using 6% p.a. simple interest.
PV = FV/(1+Rate x Time)
PV = $10,000/(1+ 6%/12 x 7)	$9,661.84
Problem 2.2 A note with a maturity value of $100,000 was purchased 46 days before maturity for $99,218.63. Calculate the rate of simple interest p.a. used
FV	$100,000.00
PV	$99,218.63
Period = 46 days/ 365 days	0.126	years
Rate
Interest rate = (FV/PV - 1) /t
Interest rate = (($100,000/$99,218.63)-1)/0.126	6.25%
Problem 2.3 Calculate the present (discounted) value at 5% p.a. payable monthly of $1,000.
(a) due at the end 4 years,
(b) due at the end 6 years.
PMT	$1,000.00
Rate = 5%/12	0.42%
period = 4 x 12	48	months
Present Value = PV(0.42%,48,-$1000)	$43,422.96	(a)
PMT	$1,000.00
Rate = 5%/12	0.42%
period = 6 x 12	72	months
Present Value = PV(0.42%,48,-$1000)	$62,092.78	(b)