1)A bank pays interest at the nominal rate of 6.5% per year. What is the effecti

Question

1)A bank pays interest at the nominal rate of 6.5% per year. What is the effective annual yield if compounding is:
ROUND ALL ANSWERS TO THE NEAREST 0.01% .
  
a) annually %
b) monthly? %
c) continuously

2)Three different investments are given in the table below.

(a) Find the balance of each investment after the two year period. Fill in correct answers in the blanks beside each investment(round all dollar figures to the nearest cent.):

Investment A

$800 deposited at 14.5% per year compounded daily (365 days per year) for two years.

$

Investment B

$925 deposited at 6.1% per year compounded continuously for two years.

$

Investment C

$1050 deposited at 3.5% per year compounded monthly for two years $

Investment A

$800 deposited at 14.5% per year compounded daily (365 days per year) for two years.

$

Investment B

$925 deposited at 6.1% per year compounded continuously for two years.

$

Investment C

$1050 deposited at 3.5% per year compounded monthly for two years $

Explanation / Answer

1.a) The effective interest yield for annually compounding will be same as nominal rate per year i.e 6.5%

b) For calculating effective interest yield monthly we will use formula

i = ( 1 + ( r / m ) )mt - 1

Where i = Interest rate

m = Compounding per period

t = Time period

= ( 1 + (6.5/12)12-1

= 6.6972%

= 6.70%( Rounded)

c) Continously

i = er - 1

Where e = 2.7182818284

i = 2.7182818284(0.065)-1

i = 6.71%

2) Investment A

A = P (1+i)n

= $1069.08

Investment B

$925 deposited at 6.1% per year compounded continuously for two years.

answer : from the above formula $1,045.02

Investment C

$1050 deposited at 3.5% per year compounded monthly for two years

Answer : $1126.02

Year Year Deposits Year Interest Total Deposits Total Interest Balance 1 $0.00 $124.81 $800.00 $124.81 $924.81 2 $0.00 $144.28 $800.00 $269.08 $1,069.08

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