Practice Test: Simple and Compound Interest
Mathematics of Business and Finance (Chapters 8 & 9)
Part 1: Multiple Choice (5 Questions)
Format: 2 Conceptual, 3 Simple Calculation
1. (Conceptual - Simple Interest) Which of the following best describes the fundamental difference between simple interest and compound interest?
a) Simple interest is calculated on the principal and accumulated interest, while compound
interest is only on the principal.
b) Simple interest is always calculated using exact days, while compound interest uses the
365-day year.
c) Simple interest is calculated only on the original principal, whereas compound interest
is calculated on the principal plus any previously earned interest.
d) Simple interest rates are always higher than compound interest rates.
2. (Conceptual - Compound Interest) If the nominal interest rate (j) remains constant, increasing the compounding frequency (m) will result in:
a) A lower effective interest rate.
b) A higher future value for a given present value.
c) A lower future value for a given present value.
d) No change in the total interest earned.
3. (Calculation - Simple Interest) Calculate the simple interest earned on a loan of £4,500 at
an annual rate of 6% for 8 months.
a) £180.00
b) £216.00
c) £270.00
d) £135.00
4. (Calculation - Compound Interest) What is the periodic interest rate (i) per quarter if the
nominal annual interest rate is 8% compounded quarterly?
a) 0.08
b) 0.04
c) 0.02
d) 0.006
5. (Calculation - Time/Periods) If an investment is held for 5 years with interest compounded
semi-annually, what is the total number of compounding periods (n)?
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a) 5
b) 10
c) 20
d) 2.5
Part 2: Long Answer - Equivalent Payments
Format: 3 Questions (Simple and Compound Interest)
6. Replacement Equation (Simple Interest)
Topic: RE = OR (Replacement Equation = Original Debt)
A business owes two debts: £3,000 due in 3 months and £5,000 due in 9 months. The business and the creditor agree to settle these debts with a single payment made 6 months from
today.
- Assume a simple interest rate of 4.5% p.a.
- Use 6 months from today as the focal date.
- Task: Calculate the size of the single replacement payment.
7. Single Payment Settlement (Compound Interest)
Topic: Single Payment / Value of Money
John wants to settle a debt of £10,000 due in 4 years. He proposes to make a single payment
today. The creditor agrees but requires an interest rate of 6% compounded monthly.
- Task: Calculate the Present Value (PV) that John must pay today to extinguish the future
debt.
8. Loan Repayment Restructuring (Compound Interest)
Topic: Loan Repayment
A company has a loan of £20,000 due today. They are unable to pay and renegotiate with
the bank to pay off the loan in two equal payments: one payment in 1 year and the second
payment in 2 years.
- The bank charges 8% compounded semi-annually.
- Let x be the size of the equal payments.
- Task: Set up the equation of value at the focal date (today) and solve for x.
Part 3: Specific Operations
Format: 4 Questions
9. Total Interest with Variable Rates
Topic: I = I1 + I2 + I3
An investor places £10,000 into a variable rate account for 3 years (simple interest). Calculate
the total interest (I) earned if the rates were:
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- Year 1 (I1 ): 3% p.a.
- Year 2 (I2 ): 4.5% p.a.
- Year 3 (I3 ): 2% p.a.
- Task: Show the summation I = I1 + I2 + I3 .
10. FV and PV over Multiple Periods
Topic: Calculate FV and PV over multiple periods
A £5,000 investment grows for 2 years at 4% compounded annually, and then the total amount
is reinvested for another 3 years at 6% compounded semi-annually.
- Step A: Calculate the Future Value (F V1 ) after the first 2 years.
- Step B: Using F V1 as the new Present Value (P V2 ), calculate the final Future Value (F Vf inal )
after the remaining 3 years.
11. Time Calculations
Topic: Solving DT1 or DT2
A promissory note is issued on March 15th (DT1 ). The term of the note is 120 days.
- Task: Determine the legal due date (DT2 ) of the note. (Assume a non-leap year).
12. Rate and Period Conversions
Topic: Solve for j or n from relationship n/t = j/i
An investment offers a nominal interest rate (j) of 12% per annum. The investment is held
for a time (t) of 4 years. If the compounding frequency is monthly:
(a) Calculate the number of periods (n).
(b) Calculate the periodic interest rate (i).
(c) Task: Demonstrate the relationship ratio. Show that:
n
j
=
t
i
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Answer Key
Part 1
1. C
2. B
8
3. A (4500 × 0.06 × 12
)
4. C (0.08 ÷ 4)
5. B (5 × 2)
Part 2
6. £7,994.48
(Bring £3k forward 3 months; bring £5k back 3 months).
7. £7,870.98
(10000 ÷ (1.005)48 )
8. £11,163.75 (approx)
Equation: 20000 = x(1.04)−2 + x(1.04)−4 .
Part 3
9. £950
(300 + 450 + 200)
10. £6,467.43
(Step A: £5,408.00; Step B: £6,467.43)
11. July 13th
(March remaining: 16 + Apr: 30 + May: 31 + June: 30 = 107 days used. 120 − 107 = 13 days
into July).
12. n = 48, i = 1%
Ratio check: 48/4 = 12 and 12/1 = 12. The ratio is 12 (the frequency m).
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