Question

What is the effective monthly interest rate for a loan with a 8%
nominal annual interest rate if the loan is compounded
**(a)** monthly, **(b)** daily, or
**(c)** continuously?

A friend offers you a loan at an effective daily interest rate
of 0.2%. **(a)** What is the nominal (also known as
the APR or Annual Percentage Rate) rate for this loan?
**(b)** What is the effective annual interest rate for
his loan?

Show all work please

Answer #1

1)

Given

Nominal annual Interest rate R=8%

a) Monthly compounding

Monthly interest rate r=8%/12=0.667%

So Effective interest rate
=(1+r)^12-1=(1+0.667%)^12-1=**8.30%**

b)

Daily compounding

Daily interest rate r=8%/365=0.0219%

So Effective interest rate
=(1+r)^365-1=(1+0.0.219%)^365-1=**8.32%**

**c)**

Continuous compounding

So Effective interest rate =e^R
-1=e^8%-1=**8.33%**

2) Effective daily rate r=0.2%

A) APR=365*r=365*0.2%=**73%**

B) Effective interest rate=
(1+r)^365-1=(1+0.2%)^365-1=**107.36%**

5) What is the effective annual interest rate for a loan with a
nominal annual interest rate of 12% if compounded:
semi-annually. Answer ____________________
monthly. Answer _________________________
continuously. Answer _____________________
6) You make a series of quarterly deposits every quarter
starting at the end Quarter 1 and ending at the end of Quarter 36.
The first deposit is $1,100, and each deposit increases by $500
each Quarter. The nominal annual interest rate is 7%, and is
compounded continuously. What is...

1. If a bank advertises a savings account that pays a 6% nominal
interest rate compounded continuously, what is the effective annual
percentage rate?
2. Bank A offers a nominal annual interest rate of 5% compounded
daily, while Bank B offers continuous compounding at a 4.6% nominal
annual rate. If you deposit $3,000 with each bank, what will be the
difference in the two bank account balances after two years?
(Show ALL work and formulas used!)

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...

1.
A bank offers 6.00% on savings accounts. What is the effective
annual rate if interest is compounded daily?
Answer Format: Percentage Round to: 4 decimal places (Example:
9.2434%
2. A bank offers 9.00% on savings accounts. What is the
effective annual rate if interest is compounded continuously?
Answer Format: Percentage Round to: 4 decimal places

If a nominal interest rate compounded quarterly is 8%, what is
the annual effective discount rate?
SHOW FORMULAS AND GET THUMBS UP

What is the effective interest rate of 8%p.a. nominal interest
rate when compounded monthly? Ans : 8.30% Pls attach the formula
used, and explain in detail. Pls do not answer in excel format.
Thank you in advance.

A loan has a stated annual rate of 17.9%. If loan payments are
made monthly and interest is compounded monthly, what is the
effective annual rate of interest? (Show your answer to the fourth
decimal place, as a decimal, NOT as a percentage. DO NOT round
until after all calculations have been completed and you have
reached your final answer.)

Find the interest rates in the following situations.
a. APR = 8%, compounded monthly. Find the effective annual
interest rate.
b. Nominal rate is 10% compounded quarterly. Find the effective
semiannual rate.
c. The effective annual interest rate is 11.02% and compounding
is monthly. Find the nominal interest rate.
d. r = 6% and compounding is monthly. Find the effective
quarterly interest rate.

The effective annual rate (EAR) for a loan with stated APR of 6%
compounded monthly is closed to:
A. 6.72%
B. 6.00%
C. 6.66%
D. 6.17%

1- For an annual interest rate of 10% compounded continuously
what it will be the effective annual interest rate?
2. For an annual interest rate of 10% compounded quarterly what
it will be the effective annual interest rate?
3. For a monthly interest rate of 1.2 % compounded quarterly
what it will be the effective annual interest rate?

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