Worksheets for Financial Mathematics

CONSUMER ARITHMETIC

Q.1. Mary earns $12.50 per hour and time-and-a half for overtime. How much does she earn in a week where she works 40 hours at regular time plus 10 hours overtime?
Q.2. Tom earns $640 per week. How much does he get if he gets his four weeks holiday pay with 17½% loading?
Q.3. Heidi earns $728 for a 40 hour week plus 8 hours overtime. If she is paid time-and-a-half for overtime what is her normal hourly rate of pay?
Q.4. The Ripemoff department store used to sell walkmans for $80.00. The manager raised the price by 20% and then advertised “20% discount” on the new price. How much would a customer now pay for a walkman?
Q.5. Stephanie bought a top for $49.50 which consists of the sale price plus 10% GST. What is the sale price?
Q.6. Sophie placed $800 in a term deposit at the bank. If her money earned 6% simple interest for 3 years how much was her final bank balance?
Q.7. Bob bought a T.V. for $5800 on time payment over 3 years at 10% simple interest.
(i) How much interest did Bob pay?
(ii) What was the total amount Bob paid for the T.V.?
(iii) What was the amount of Bob’s monthly repayments (to the nearest 5cents)?
Q.8. Lisa earned $16.80 per hour for a 40 hour week. Tax of $134.40 was deducted from her gross wage. Also 8% of her gross wage was paid into a special superannuation account.
(i) How much superannuation did Lisa pay for the week?
(ii) How much did Lisa receive in her pay packet (to nearest 5 cents)?
Q.9. (i) Write down the formula for compound interest.
(ii) Bert invested $1000 at 6% compound interest for 10 years. What was his investment worth at the end of this time?
(iii) Simone invested $1000 at 7% simple interest for 10 years. What was her investment worth at the end of this time?
Q.10. Becky was paid $2538 that consisted of 3 weeks pay plus a 17½% holiday loading. What was Becky’s weekly rate of pay?
ANSWERS:
Q.1. $687.50 Q.2. $3008 Q.3. $728 Q.4. $76.80 Q.5. $45.00 Q.6. $944
Q.7. (i) $1740 (ii) $7540 (iii) $209.45 Q.8. (i) $53.76 (ii) $483.85
Q.9. (i) A = P ( 1 + r/100 )n where A = final amount P = principal r = rate %
n = number of compounding periods, usually years. (ii) $1790.85 (iii) $1700 Q.10. $720

INTEREST

Simple Interest: I = (Prn)/100 where
I = Simple Interest
P = Principal,
r = rate per interest period (usually a year),
n = number of interest periods.

Example: What will be the value of $2000 invested for 5 years at 6% p.a. simple interest?
I = (Prn)/100 = 2000x6x5/100 = 600
Amount = Principal + Interest = $2000 + $600 = $2600

Exercises 1:
Q.1. If I invest $600 at a simple interest rate of 7% p.a., how much will I have in the account after 10 years?
Q.2. Ryan invested $50 in a bank account that paid 4% p.a. simple interest. How much would it be worth after 9 months?
Q.3. What simple interest rate would be required to double the amount of the investment in 20 years?
Compound Interest: A = P(1 + r)ⁿ where
A = final amount,
P = Principal,
r = rate As a decimal,per interest period (usually a year),
n = number of interest periods.
Compound interest is where you earn interest on your interest.
Example: What will be the value of $2000 invested for 5 years at 6% p.a. compound interest?
A = p(1 + r)ⁿ = 2000(1 + 0.06)⁵ = 2000(1.06)⁵ = $2676.45

Exercises 2:
Q.1. If I invest $600 at a compound interest rate of 7% p.a., how much will I have in the account after 10 years?
Q.2. Josh invested $50 in a bank account that paid 4% p.a. compound interest. How much would it be worth after 5 years?
Q.3. Chris invested $5000 for 6 years at 6% p.a. compound interest. What was the final value of the account?
Q.4. Karen invested $5000 for 6 years in an account where the 6% p.a. interest was compounded every 6 months. What was the final value of the account?
Answers:
Ex.1 Simple Interest: Q.1. = $1020 Q.2. = $51.50 Q.3. = 5%
Ex. 2. Compound Interest: Q.1. = $1180.29 Q.2. = $60.83
Q.3. = $7092.60 Q.4. = $7128.80

INTEREST 2

Compound Interest: A = P(1 + r)ⁿ where
A = final amount,
P = Principal,
r = rate as a decimal, per interest period (usually a year),
n = number of interest periods.
Compound interest is where you earn interest on your interest.
Example: What will be the value of $5000 invested for 10 years at 5% p.a. compound interest?
A = P(1 + r)ⁿ = 5000(1 + 0.05)¹⁰ = 5000(1.05)¹⁰ = $8144.47
Exercises:
Q.1. If I invest $200 at a compound interest rate of 8% p.a., how much will I have in the account after 10 years?
Q.2. Josh invested $100 in a bank account that paid 5% p.a. compound interest. How much would it be worth after 4 years?
Q.3. Chris invested $10 000 for 20 years at 6% p.a. compound interest. What was the final value of the account?
Q.4. Karen invested $10 000 for 20 years in an account where the 6% p.a. interest was compounded every 6 months. What was the final value of the account?
Q.5. Michelle invested $10 000 for 20 years in an account where the 6% p.a. interest was compounded every month. What was the final value of the account?
The compound interest formula can also be used to determine depreciation. In this case the rate is subtracted.
Depreciation: A = P(1 - r)n where
A = final value,
P = Initial cost,
r = rate per depreciation period (usually a year),
n = number of depreciation periods.
Example: A photocopier costs $4 000 and depreciates at the rate of 20% per year. How much is it worth after 5 years?
A = P(1 – r)ⁿ 4000(1 – 20/100)⁵ = 4000(0.8)⁵ = $1310.72
Exercises.
Q.1. Simone bought a walkman for $120. If it depreciates at the rate of 15% per year, how much is it worth after 3 years.
Q.2. Emma bought a car for $8000. If it depreciates at the rate of 12% per year, how much will it be worth after 10 years.
Q.3. Lauren bought a sound system for $3 800. If it depreciates at the rate of 1% per month, how much will it be worth after 2 years?
Answers: Compound Interest: Q.1. = $431.78 Q.2. = $121.55 Q.3. = $32071.35 Q.4. = $3260.38 Q.5. = $33102.04
Depreciation: Q.1. = $73.70 Q.2. = $2228.01 Q.3. = $2985.58