Question

1. What nominal rate compounded annually would
quadruple the principal in 4

years?

2. A master card compounds monthly and charges an interest of 1.5%
per month.

What is the effective interest rate per year?

3. How long will it take money to triple itself if invested at 8%
compounded

annually?

4. Microsoft CEO, billionaire Bill Gates willed that a sum of $25
million be given to a

child but will be held in trust by the child’s mother until it
amounts to $45 million. If

the amount is invested and earns 8% compounded quarterly, when will
the child

receive the money?

5. A credit plan charges interest rate of 36% compounded monthly.
Find its effective

rate.

6. Find the amount at the end of two years and seven months if
P1000 is invested

at 8% compounded quarterly using simple interest for anytime less
than a year

interest period.

7. A P2000 loan was originally made at 8% simple interest for 4
years. At the end of

this period the loan was extended for 3 years without the interest
being paid, but

the new interest rate was made 10% compounded semiannually. How
much

should the borrower pay at the end of 7 years?

Answer #1

**1)** Let interest rate be "r" compounded
annually

4P = P * (1 + r)^^{4}

4 = (1 + r)^^{4}

Taking (1/4) of the root on both sides:

1 + r = 1.4142

r = 0.4142 which is 41.42%

**2)** Interest rate = 1.5% per month

Annual effective rate of interest: [1 + Monthly rate of
Interest]^^{Number of compounding done in an year} = [1 +
0.015]^^{12} = 1.1956 which is 19.56%

**3)** Let interest rate be "r" compounded
annually

3P = P * (1 + r)^^{3}

3 = (1 + r)^^{3}

Taking (1/3) of the root on both sides:

1 + r = 1.4422

r = 0.4422 which is 44.22%

**4)** Interest rate = 8% compounded quarterly
which means annual effective rate of interest is [1 + (8% /
2)]^^{4} = 1.0824 which is 8.24%

Amount Invested = 25 million

45 = 25 * 1.0824^^{n} where "n" is number of years after
which child recieve the money

n = 7.42 years

1. Suppose that P200,000.00 is invested at a certain rate of
interest compounded annually for two years. If the accumulated
interest at the end of 2 years is P42,000.00, find the rate of
interest.
2. A loan for P170,000 is to be paid in three years
at the amount of P185,000 compounded annually. What is the
effective rate of money?
3. If P3000 accumulates to P4500 when invested at a simple
interest for ten years, what is the rate of interest?

Find the amount at the end of two years and seven months if
P1000 is invested at 8% compounded quarterly using simple interest
for anytime less than a year interest period.

1.An investment will quadruple your money in 12 years. What is
the nominal rate of interest convertible quarterly?
Answer = % (3 Sig Fig)
2.AJ takes out a small business loan of $15000 at a nominal rate
of interest of 10.6% convertible quarterly. One year later, he
repays $ 3500. Two years after that, the bank wants to sell AJ's
loan to another institution. How much does AJ owe at that
time?
Answer = dollars. (3 Sig Fig)

An investment promises to quadruple your money in nine years. If
the interest is compounded monthly, what effective annual rate
would you earn? (Hint: Calculate the monthly rate and convert that
to the effective annual rate, EAR.) A. 25.99% B. 16.65% C. 18.92%
D. 21.90% E. 31.95% F. 41.42%

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?
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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...

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gift of a trip to Canada for her husband at the end of 10 years.
She will have enough to pay for the trip if she invests $4,000 per
year until that anniversary and plans to make her first $4,000
investment on their first anniversary. Assume her...

What is the future value of $100 invested at 10% compounded
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What is the future value of $100 invested at 10% compounded
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You end up with $20,000 after investing for 20 years at 8%
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Maverick Jane places $800 in a savings account paying 6%...

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b) 8% for 2 periods
c)2% for 8 periods
d)8% for 4 periods
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1)Hewlett Plastics Inc. received a loan of $60,000 at 3.75%
compounded quarterly to purchase machinery for its factory.
Calculate the time period of the loan if the total interest paid
was $32,165.48.
2)How long would it take for an investment to double its
original amount at 3.62% compounded monthly?
3)Calculate the effective interest rate for each of the
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a. 2.16% compounded quarterly.
Round to two decimal places
b. 2.16% compounded monthly.
4)Lucy invested $210,000 to purchase...

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