Question

What is the APR if your bank wants to earn an EAR of 7.90% on
the loans, compounding quarterly?

Answer #1

APR = 7.676% per annum compounded quarterly

**Concept**

Effective Annual Rate = [1 + (APR / Number of compounding in a year)]^Number of compounding in a year - 1

**Solution**

We are given the following information

EAR = 7.9% or 0.079

No of compounding in a year = 4

Putting this two information in the equation

Effective Annual Rate = [1 + (APR / Number of compounding in a year)]^Number of compounding in a year - 1

0.079 = [1 + (APR/4)]^4 - 1

1.079^(1/4) = 1 + (APR/4)

1.01919 = 1 + (APR/4)

0.01919 = APR / 4

**APR = 0.07676 or 7.676% per annum compounded
quarterly**

Calculating EAR Find the EAR in each of the following cases:
Stated Rate (APR) # Compounding Periods 8.55% Quarterly 11.45%
Monthly 8.77% Daily
Show All Work

8. A given rate is quoted as 12% APR, but has an effective
annual rate (EAR) of 12.55%. What is the frequency of compounding
during the year? a. Annually b. Semiannually c. Quarterly d.
Monthly e. Daily

Straight bank loan. Right Bank offers EAR loans of
8.74 % and requires a monthly payment on all loans. What is the APR
for these monthly loans? What is the monthly payment for a loan of
(a) $235,000 for 6 years,
(b) $465,000 for 14 years, or
(c) $1,450,000 for 28 years?

Straight bank loan. Right Bank offers EAR loans of 8.99 % and
requires a monthly payment on all loans. What is the APR for these
monthly loans? What is the monthly payment for a loan of (a) $
230,000 for 7 years, (b) $ 455,000 for 12 years, or (c) $
1,500,000 for 32 years?

Right Bank offers EAR loans of 8.98% and requires a monthly
payment on all loans. What is the APR for these monthly
loans? What is the monthly payment for a loan of
(a) $250,000 for 5 years,
(b) $450,000 for 11 years
(c) $1,450,000 for 32 years?

What is the difference between APR on the following loans?
(Difference = higher APR - lower APR)
Option 1
Borrow $70,000
Repay $80,000
Time 5 years
Annual compounding
Option 2
Borrow $75,000
Repay $85,000
Time 5 years
Quarterly compounding

Your work for a bank that requires 30-year mortgages to have an
EAR of 6.676%. The mortgages have monthly payments (and monthly
compounding).
(a) What is the APR of these mortgages?
(b) A customer closes a deal to purchase a $800,000 home with
20% down. Her first payment is one month from now. Ignoring taxes
and insurance, what are her monthly mortgage payments be?

APR
EAR
APR
APR
A. 7.00% B. 7.24% C. 7.49% D. 7.95%
Question 8. You would like to buy an apartment
in five years, and you are starting to save to finance the down
payment. You already have €12,000 on a savings account in which you
are planning to make additional annual deposits of €7,500 during
the next five years (first deposit in t=1). If the savings account
pays an annual interest rate of 4%, what will its balance be...

Vandermark Credit Corp. wants to earn an effective annual return on
its consumer loans of 13.9 percent per year. The bank uses daily
compounding on its loans. What interest rate is the bank required
by law to report to potential borrowers?
A)
12.43%
B)
13.02%
C)
14.90%
D)
15.72%
E)
16.46%

Bank 1 is offering loans at 2% APR with monthly compounding.
Bank 2 has a CD paying an interest rate of 3% APR with semi-annual
compounding. Can you make a riskless profit by borrowing and
lending? Suppose you borrowed $10,000 from Bank 1 and invested it
in Bank 2. How much money will you have after one year?

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