1.
Find the present value of payments of $250 at the end of years 1 to 4 and $350 at the end of years
5 to 11 if:
a) The interest rate is 7% per annum
b) The interest rate is 8% per annum for the first 4 years and 6% per annum thereafter
c) The interest rate is 9% per annum for the first 6 years and 7% per annum thereafter
2.
Calculate the accumulated value at the end of 25 years of the following payments:
100 per annum payable annually in advance for years 1 to 10, and
150 per annum payable annually in advance for years 11 to 20
Given that the effective rate of interest is:
9% per annum for the first six years,
7% per annum for the following nine years, and
5% per annum thereafter
3.
An investor pays $50 into savings plan at the beginning of each quarter year for 10 years.
If the investment accumulates at 9% per annum convertible quarterly, calculate the amount
in the savings plan after 10 years.
4.
a) Show that
b) Hence, or otherwise, if 7.620224 and =10.790191, find and
5.
Using an effective rate of interest of 6% per annum, find the present value of an annuity of 100 per
annum payable at the end of every three years for 60 years.
6.
An 10-year annuity makes payments annually in arrears.
The amount of the first payment is $1000 with payments increasing by $50 each year (so
that the final payment at time 10 is of amount $1450).
Using a rate of interest of 9% per annum, find the present value of this annuity
7.
If the interest rate is 5% per annum convertible every two years, calculate the present value of:
a) $100 per annum payable quarterly in arrears for 20 years
b) $100 per annum payable every two years for ten payments, with the first payment being
made exactly one year from now
8.
Using an interest rate of 7% per annum, find the present value of fifteen payments of amount $300
each payable every three years, with the first payment made at the end of the second year.
9.
A 20-year annuity-due provides annual payments in advance starting at $250 in year 1, reducing by
$20 per annum until the annual payment is $70, and then remaining at $70 until the 20th and final
payment has been made.
Show below three suggested expressions for the present value of the annuity.
a) 70 +20
b) 250 20 180
c) 270 20 70
Which of the expressions are correct?
a) a and b only are correct
b) a and c only correct
c) b and c only are correct
d) all three are correct
10.
What is the accumulated value of an annuity of $12 per annum payable quarterly in arrears
for 15 years, using a rate of interest of 12% per annum convertible half- yearly?
a) $467.01
b) $481.36
c) $489.16
d) $493.73
11.
Using an effective rate of interest of 5% per annum, what is the value of ?
a) 100.93
b) 104.67
c) 107.26
d) 113.70
Explain in words exactly what the notation represents.
12.
Using a rate of interest of 4.7% per annum, what is the value of ?
a) 4.1924
b) 4.3408
c) 4.4416
d) 4.5958
Explain in words exactly what the notation represents.