Joy is taking out a car loan which she will pay back with interest. Which option will require her to pay the lowest amount in interest? Annual Compounding Semi-Annual Compounding Monthly Compounding Daily Compounding
Answers
To answer this we can have an example to prove our answer.
Let the principle amount be 100.
Let the rate of interest be 2%
Let the period be 1 year.
The compound interest formula is :
A (n) = P(1 + i)ⁿ
1) Annual compounding.
A = 100 × (1.05) = 105
Interest = 105 - 100 = 5
2) Semi annual compounding
A = 100(1 + 0.05/2)
A = 100 (1.025)² = 105.0625
Interest = 5.0625
3) Monthly compounding
A = 100(1 + 0.05/12)¹² = 100 × 1.05116
= 105.116
Interest = 5.116
4)Compounding daily
A = 100(1 + 0.05/365.25)^365.25
A = 100 × 1.05127 = 105.127
Interest = 5.127
From the analysis above we see that the daily compounding has the highest amount of interest.
The lowest interest is paid when the compounding is done annually.
The correct answer is A.
If she chooses annual compounding, it will be the most profitable way because she has to pay a meager rate of interest.
When compared to the given four answers the lowest will be when she chooses the annual compounding.
Hence you can pick the correct answer is A.