Last time. . .
Principal: the initial amount invested.
Period: how often interest is paid.
Periodic rate: the interest received each period, as a
proportion of the balance.
Nominal [annual] rate, or APR: a not very useful number,
but the way that interest
Loan repayments. Finding payments on a loan.
Total interest. (aka nance charge)
Amortisation. Breaking down repayments as an
Example: Amortisation, contd
Problem. Dave amortises a loan of $170,
Annuities. Ordinary annuities, annuities due. Examples.
1 (1 + r)n
Present value. A = R
= Ran|r .
Generalised annuities. Directly; or in terms of ordinary
Example: Annuity due
Problem. The premiums of an insurance policy are $5
Last time, and since:
Annuitites due. Connections with ordinary annuities.
(1 + r)n 1
Future value. S = R
= Rsn|r .
Practice problems: None covered from Fri 16.
Exam dates. First midterm: Wed 12 Oct (just after
Thanksgiving.) Second midt
So far: Ch. 5
Compound interest. Nominal, periodic, effective interest
rates. Ordinary and continuous compounding.
Effect of time on value. Present and future values.
Timelines. Equations of value.
Annuities. Present and future values; an|r , sn|r . Diffe
Last time: outline of row-reduction
1. Represent system of equations by augmented matrix (i.e. a
matrix and a vector together).
2. Use elementary row operations to put the matrix into
3. Turn the augmented matrix back into equations;
Net Present Value. Comparing present values to
determine protability of an investment.
Continuous compounding. S = Pert .
Annuities. Example: pension plan.
Example: Pension plan
Problem. A certain pension plan pays out $3,000 at the end of