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**

Pl. repost other unanswered question for their proper answers!

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?...

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monthly.
2. A Credit Card company says their card charges an APY of
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(Show ALL work and formulas used!)

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Show all work please

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monthly. Answer _________________________
continuously. Answer _____________________
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Quarterly
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Monthly
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question here

There are four banks: A, B, C and D:
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