Question

For a deposit of $1027 at 6.4% over 2 years, find the interest earned if interest is compounded semiannually, quarterly, monthly, daily, and continuously.

The interest earned if interest is compounded semiannually is----

2

Find the present value of the following future amount.

$2000 at 10% compounded annually for 30 years

The present value is-----

3 Suppose a savings and loan pays a nominal rate of

1.4%

on savings deposits. Find the effective annual yield if interest is compounded quarterly

The effective annual yield is------

4

How long would it take to double your money in an account paying

3%

compounded quarterly

Ignoring leap years, the investment will be doubled in------years and---- days

Answer #1

1. For a deposit of $1027 at 6.4% over 2 years, find the interest earned if interest is compounded semiannually, quarterly, monthly, daily, and continuously.

The interest earned if interest is compounded semiannually is = Effective compounded interest = ( 1 + r / m)n - 1

n = number period we get interest = semiannually of two years = 4

m = how much time compound in a year = 2 = 12 / 6 = 2

Effective compounded interest = ( 1+ 6.4% / 2)4 - 1 = ( 1 + 3.2% )4 - 1 = 1.1342 - 1 = 0.1342 = 13.42%

The interest earned if interest is compounded semiannually is
**= 1027 * 13.42% = 138**

The interest earned if interest is compounded quarterlly is =

n = 2 * 4 = 8

m = 12 / 4 = 4

= (1+ 6.4% / 4)8 - 1 = 1.1354 - 1 = 0.1354 = 13.54%

The interest earned if interest is compounded quarterlly is = 1027 * 13.54% = 139

2. Find the present value of the following future amount. $2000 at 10% compounded annually for 30 years

The present value is-----

PV of Annuity = (A / r )(1 - 1 / ( 1+r)n)

or

PV of Annuity = Amount * ( 1/1+ r)nGT

**= 2000 * ( 1/1 + 10%)30GT = 2000 * (1/1.1)30GT = 2000 *
9.4269 = 18854**

GT = grand total (calculator fuction)

3. Suppose a savings and loan pays a nominal rate of 1.4% on savings deposits. Find the effective annual yield if interest is compounded quarterly

The effective annual yield is- = ( 1 + r / n )n - 1 n =12 /4 = 4

= ( 1 + 1.4% / 4)4 - 1 = ( 1 + 0.35%)4 - 1

= (1.0035)4 - 1

= 1.01407 - 1 = 0.0141 = 1.41%

3. How long would it take to double your money in an account paying 3% compounded quarterly

Annual effective interest = ( 1 + 3% / 4)4 - 1 = (1+0.75% )4 - 1 = 1.0303 - 1 = 0.0303 = 3.03 %

we can solve it with example, for that we use $ 100 as amt deposite and we need to double our money to $ 200,

For calculation we use a formula

Amount(double the p) = principle ( 1 + r )n

200 = 100 ( 1+ 3.03% )n

Here we need to find the n = number of quarters take to double our money

= 200 / 100 = (1.0303)n

= 2 = (1.0303)n

Here we use log fuction of calculator

=log 2 / log 1.0302 = n

n = 23.22 quarters

which mean 23.22 / 4 = 5.805 years

= 5 years and 365 * 0.805 = 294 days

**Ignoring leap years, the investment will be doubled in
--5----years and 294 days**

Find the interest earned on $25000.00 invested for 6 years at
4.5% interest compounded as follows.
a. Annually -Compounding annually, the interest earned is
b. Semiannually (twice a year) -Compounding semiannually, the
interest earned is
c. Quarterly -Compounding quarterly, the interest earned is
d. Monthly- Compounding monthly, the interest earned is
e. Continuously- . Compounded continuously, the interest earned
is

You deposit $300 in an account earning 7% coumpound interest for
2 years. Find the future value and the interest earned for each of
the following compounding frequencies. Use the Bankers' Rule for
daily compounding.
Frequency
Future Value
Interest Earned
Annually:
Semiannually:
Quarterly:
Monthly:
Daily:

16. You have $1,000 to deposit in a savings account for 1 year.
You can get a passbook savings
account drawing 7.75% interest compounded continuously, or a
certificate of deposit paying 8%
compounded quarterly, or a savings bond paying 8.25% compounded
annually. Which alternative
should you take?
a. 7.75% compounded continuously
b. 8% compounded quarterly
c. 8.25% compounded annually
d. all of the above are have equal annualized yields
17. You are considering two investments described below:
Investment
A 10%...

Present Value Computation
Pete Frost made a deposit into his savings account 3 years ago, and
earned interest at an annual rate of 8%. The deposit accumulated to
$20,000. How much was initially deposited assuming that the
interest was compounded (a) annually, (b) semiannually, and (c)
quarterly?
Use Excel or a financial calculator for computation. Round your
answer to nearest dollar.
(a)
Annually
Answer
(b)
Semiannually
Answer
(c)
Quarterly
Answer

Present Value Computation
Pete Frost made a deposit into his savings account 3 years ago, and
earned interest at an annual rate of 8%. The deposit accumulated to
$21,000. How much was initially deposited assuming that the
interest was compounded (a) annually, (b) semiannually, and (c)
quarterly?
Use Excel or a financial calculator for computation. Round
your answer to nearest dollar.
(a)
Annually
Answer
(b)
Semiannually
Answer
(c)
Quarterly
Answer

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...

Find the compound amount for the deposit and the amount of
interest earned. $7600 at 8 % compounded quarterly for 8 years. The
compound amount after 8 years is?
(Do not round until the final answer. Then round to the nearest
cent as needed.)
The amount of interest earned is
(Do not round until the final answer. Then round to the nearest
cent as needed.)

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!)

Find the accumulated value of an investment of $ 25,000 for 3
years at an interest rate of 7% if the money is a. compounded
semiannually b. compounded quarterly c. compounded monthly d.
compounded continuously.

Find the interest earned at 6.25% interest rate compounded
continuously for 4 years, of the continuous income stream with rate
of flow f(t)=1650e-.02t

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