Question

Exercise IV (effective and nominal interest rate)

a. The effective interest rate is 21.44%. If there are 12 compounding periods per year, what is the nominal interest rate?

b. What is the effective interest rate on a continuously compounded loan that has a nominal interest rate of 25%?

c. Which is the better investment, a fund that pays 20% compounded annually, or one that pays 18.5 % compounded continuously?

d. Money invested at 6% per year, compounded monthly. How money months you need to triple your money?

e. One thousand dollars is deposited into an account that pays interest monthly and allowed to remain in the account for three years. The balance at the end of the three years is $1,544.00. What is the nominal interest rate paid on this account?

Answer 1

A.

Let, nominal interest rate = K

Then,

21.44% = (1+ K/12)^12 -1

K/12 + 1 = 1.2144^(1/12) = 1.016319

K = 12*.016319 = 19.58%

So, nominal annual interest rate is 19.58%

B.

Effective interest rate (annual) = e^.25 - 1 = 2.71828^.25 – 1

Effective interest rate (annual) = 28.40%

C.

When firm pays 18.5% with continuous compounding.

Effective annual interest rate = 2.71828^.185 – 1 = 20.32%

Since the effective interest rate of 20.32% is better than interest rate of 20% compounding annually, then it is better to choose 18.5% interest rate with continuous compounding.

D.

Monthly interest rate = 6%/12 = .5%

Let, is it is n month to triple the money

3 = (1+ .5%)^n

n = log 3 / log 1.005

n = 220.27 months

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