Question

Ellen has recently inherited $5400, which she wants to deposit into a CD account. She has determined that her two best bets are an account that
compounds semi-annually at an annual rate of 4.1 % (Account 1) and an account that compounds quarterly at an annual rate of 5.3%. Which account would pay Ellen more interest?​

Answer 1

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 × $\left( 1 + \frac{r}{n} \right)^{\Large{n\times t}}$ - Principle

on substituting the respective values, we get

Interest = $5400 × $\left( 1 + \frac{0.041}{2} \right)^{\Large{2\times1}}$ - $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 × $\left( 1 + \frac{r}{n} \right)^{\Large{n\times t}}$ - Principle

on substituting the respective values, we get

Interest = $5400 × $\left( 1 + \frac{0.053}{4} \right)^{\Large{4\times1}}$ - $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