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

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%...

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:

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...

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

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.

Find the nominal annual rate of interest
a) at which $1500 will grow to $1800 in four years compounded
compounded monthly
b) at which money will double in seven years if compounded
quarterly

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

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!)

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