Question

Periodic interest rates. You have a savings account in which you leave the funds for one year without adding to or withdrawing from the account. Which would you rather​ have: a daily compounded rate of 0.050​%, a weekly compounded rate of 0.355​%, a monthly compounded rate of 1.25​%, a quarterly compounded rater of 4.25​%, a semiannually compounded rate of 7%, or an annually compounded rate of 15​%?

What is the effective annual rate​ (EAR) of a daily compounded rate of 0.050​%?

______​% ​(Round to two decimal​ places.)

Answer 1

Compounding = P*(1+r/n)^nt

Where,

P = Principal amount,

R = Rate of interest

n = number of year

t = Times compounded

Lets apply the formula for each of the above cases with an assumption of taking Principal amount as $100 for all the cases:

1. Daily compounding r = 0.050%, t=365

Compound amount = 100*(1+(0.0005/1))^365

Compound amount = $120.02

Interest = $20.02(120.02-100)

2. Weekly compounding r = 0.355%, t=52

Compound amount = 100*(1+(0.00355/1))^52

Compound amount = $120.23

Interest = $20.23(120.23-100)

3. Monthly compounding r = 1.25%%, t=12

Compound amount = 100*(1+(0.0125/1))^12

Compound amount = $116.08

Interest = $16.08(116.08-100)

4. Quarterly compounding r = 4.25%, t=4

Compound amount = 100*(1+(0.0425/1))^4

Compound amount = $ 118.11

Interest = $18.11(118.11-100)

5. Semi-Annualy compounding r = 7%, t=2

Compound amount = 100*(1+(0.07/1))^2

Compound amount = $ 114.49

Interest = $14.49(114.49-100)

6 For annualy we can directly take $ 115, Interest = $15(115-100)

From the above results a rational person will go for the option which can earn him more. Here interest rate of 0.355% compounded weekly will earn more interest as compared to other rates. So it is recomended to go for weekly compounded rate of 0.355%

Effective annual rate of daily compounded rate of 0.050% = 20.02% from 1 above we can directly compute it.