Answer:
Interest for case 2 is more i.e at interest rate 5.3% compounded quarterly
Step-by-step explanation:
Data provided in the question:
Principle amount = $5400
let us calculate the interest for t = 1 year
Case 1:
Rate of interest, r = 4.1%
Compounded semi-annually i.e number of periods, n = 2
Therefore,
Interest = Principle × [tex]\left( 1 + \frac{r}{n} \right)^{\Large{n\times t}}[/tex] - Principle
on substituting the respective values, we get
Interest = $5400 × [tex]\left( 1 + \frac{0.041}{2} \right)^{\Large{2\times1}}[/tex] - $5400
or
Interest = $5400 × 1.0205² - $5400
or
Interest = $5623.67 - $5400
= $223.67
Case 2:
Rate of interest, r = 5.3% = 0.053
Compounded quarterly i.e number of periods, n = 4
Therefore,
Interest = Principle × [tex]\left( 1 + \frac{r}{n} \right)^{\Large{n\times t}}[/tex] - Principle
on substituting the respective values, we get
Interest = $5400 × [tex]\left( 1 + \frac{0.053}{4} \right)^{\Large{4\times1}}[/tex] - $5400
or
Interest = $5400 × 1.01325⁴ - $5400
or
Interest = $5691.94 - $5400
= $291.94
Hence,
interest for case 2 is more i.e at interest rate 5.3% compounded quarterly
