📝 Chapter 6: Financial Mathematics

Assessment AS Learning — Practice Quiz

🔄 Not Graded — Unlimited Retakes

Purpose: Self-check compound interest, present value, and ordinary annuities.

Score: 0 / 12

Compound Interest

Question 1

For 8% per annum compounded quarterly for 5 years: $ i = ? $

Solution:

$ i = 0.08/4 = 0.02 $ per quarter.

Question 2

For Q1, the number of compounding periods $ n $ is:

Solution:

$ n = 5 \times 4 = 20 $.

Question 3

\$1500 invested at 5% per year compounded annually for 10 years gives (round to nearest dollar):

Solution:

$ A = 1500(1.05)^{10} \approx 1500(1.6289) \approx \$2443 $.

Question 4

How much should be invested today at 6% compounded annually to have \$5000 in 8 years (round to nearest dollar)?

Solution:

$ P = 5000(1.06)^{-8} \approx \$3137 $.

Annuities — Future Value

Question 5

Saving \$200 at the end of each year for 10 years at 5% compounded annually gives FV $\approx$ (nearest dollar):

Solution:

$ FV = 200 \cdot \frac{(1.05)^{10} - 1}{0.05} \approx 200 \cdot 12.578 \approx \$2516 $.

Question 6

Saving \$100/month for 5 years at 6% per year compounded monthly gives FV (nearest dollar):

Solution:

$ i = 0.005, n = 60 $. $ FV = 100 \cdot \frac{1.005^{60} - 1}{0.005} \approx \$6977 $.

Annuities — Present Value & Mortgages

Question 7

PV of \$500/year for 10 years at 4% compounded annually (nearest dollar):

Solution:

$ PV = 500 \cdot \frac{1 - 1.04^{-10}}{0.04} \approx 500 \cdot 8.111 \approx \$4055 $.

Question 8

A loan of \$10{,}000 at 6% per year compounded monthly is repaid over 5 years. Monthly payment (nearest dollar):

Solution:

$ i = 0.005, n = 60 $. $ R = \frac{10000}{(1 - 1.005^{-60})/0.005} \approx \$193.33 $.

Question 9

Effective annual rate of 12% compounded monthly (round to two decimals as %):

Solution:

$ (1.01)^{12} - 1 \approx 0.1268 $, so $ \approx 12.68\% $.

Question 10

Which compounding gives the highest amount at 6% per year over 1 year?

Annual
Quarterly
Monthly
Daily

Solution:

More frequent compounding → larger effective rate. Daily is highest of these.

Question 11

Doubling time at 6% compounded annually (use rule of 72):

Solution:

$ 72/6 = 12 $ years.

Question 12

Which formula gives the present value of an ordinary annuity?

$ PV = R \cdot \frac{(1+i)^n - 1}{i} $
$ PV = R \cdot \frac{1 - (1+i)^{-n}}{i} $
$ PV = R \cdot (1+i)^n $
$ PV = R/i $

Solution:

The PV-annuity formula is $ PV = R \cdot \frac{1 - (1+i)^{-n}}{i} $. Option (a) is the FV formula.