Grade 12 Financial Maths – Question 3 draws its questions at random from a bank of 18 questions, with full worked solutions for every one.
A few of the question types, with full solutions, so you know what to expect.
Joseph opens a savings account at a nominal interest rate of 6% p.a., compounded quarterly. Determine the effective annual interest rate.
Answer: 6,14% per annum
Use: \( (1+i_{eff}) = \left(1+\dfrac{i_{nom}}{m}\right)^m \)
Substitute \( i_{nom}=0{,}06,; m=4 \):
\( (1+i_{eff}) = (1{,}015)^4 \)
\( i_{eff} = 1{,}06136...-1 \)
A bank offers 8% p.a. compounded monthly. What is the effective annual interest rate?
Answer: 8,30% per annum
\( (1+i_{eff})=\left(1+\dfrac{0{,}08}{12}\right)^{12} \)
\( i_{eff}=1{,}08299...-1 \)
An investment earns 12% p.a. compounded semi-annually. Determine the effective annual interest rate.
Answer: 12,36% per annum
\( m=2:; (1+i_{eff})=(1{,}06)^2=1{,}1236 \)
An account offers 10% p.a. compounded daily (365 days). What is the effective annual interest rate?
Answer: 10,52% per annum
\( (1+i_{eff})=\left(1+\dfrac{0{,}10}{365}\right)^{365} \)
\( i_{eff}=1{,}10516...-1 \)
An account offers 9% p.a. compounded monthly. What is the effective annual interest rate?
Answer: 9,38% per annum
\( (1+i_{eff})=\left(1+\dfrac{0{,}09}{12}\right)^{12} \)
\( i_{eff}=1{,}09381...-1 \)