Question

What is continuous compounding? How does the APY for continuous compounding compare to the APY for, say, daily compounding? Explain the formula for continuous compounding.

Answer #1

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For rate of interest r , if we take compounding period infinite ... So that means continous compounding...

Simply we say that this is compound interest value when we take compounding period infinite..

In above example , very small difference in daily compounding and continous compounding..

Because as we increase no of periods , compound interest vue come closer to continous compounding value..

Formula for continous compounding is

Future value = present value * e^(r*t) ....

Consider an account with an APR of 4.6%. Find the APY with
quarterly compounding, monthly compounding, and daily
compounding. Comment on how changing the compounding period affects
the annual yield

Consider an account with an APR of 6.8%. Find the APY with
quarterly compounding, monthly compounding, and daily
compounding. Comment on how changing the compounding period affects
the annual yield. When the interest is compounded quarterly," What
is the APR"?

Use the formula for continuous compounding to compute the
balance in the account after? 1, 5, and 20 years.? Also, find the
APY for the account. A?=$17,000 deposit in an account with an APR
of 3.75?%.

Use the formula for continuous compounding to compute the
balance in the account after 1, 5, and 20 years. Also, find the
APY for the account. A $2000 deposit in an account with an APR of
3%. The balance in the account after 1 year is approximately
[...]

Use the formula for continuous compounding to compute the
balance in the account after 1, 5, and 20 years. Also find the APY
for the account.
A $3000 deposit in an account with an APR of 8%
Year 1 =
Year 5+
Year 20=

Use the formula for continuous compounding to compute the
balance in the account after 1, 5, and 20 years. Also, find the
APY for the account. A $7000 deposit in an account with an APR of
3.3%.
The balance in the account after 1 year is approximately $
The balance in the account after 5 years is approximately $
The balance in the account after 20 years is approximately $
(Round to the nearest cent as needed.)

Direction: Compounding More than once a Year. Use the
appropriate compound interest formula to compute the balance in
each account after the stated period of time.
1.) $10,000 is invested for 5 years with an APR of
2.75% and monthly compounding.
Directions: Annual Percentage Yield (APV). Find the annual
percentage yield (to the nearest 0.01%) in each case.
1.) A bank offers an APR of 3.2% compounded
monthly.
Directions: Continuous Compounding. Use the formula for
continuous compounding to compute the...

Direction: Compounding More than once a Year. Use the
appropriate compound interest formula to compute the balance in
each account after the stated period of time.
1.) $10,000 is invested for 5 years with an APR of
2.75% and monthly compounding.
Directions: Annual Percentage Yield (APV). Find the annual
percentage yield (to the nearest 0.01%) in each case.
1.) A bank offers an APR of 3.2% compounded
monthly.
Directions: Continuous Compounding. Use the formula for
continuous compounding to compute the...

5A-1
FV CONTINUOUS COMPOUNDING If you receive $15,000 today and can
invest it at a 6% annual rate compounded continuously, what will be
your ending value after 15 years?
5A-2
PV CONTINUOUS COMPOUNDING In 7 years, you are scheduled to
receive money from a trust established for you by your
grandparents. When the trust matures there will be $200,000 in the
account. If the account earns 9% compounded continuously, how much
is in the account today?
5A-3
FV CONTINUOUS COMPOUNDING...

1. An interest rate is 5% per annum with continuous compounding.
What is the equivalent rate with semiannual compounding?

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