Question

11.) You have steady employment and earn a regular salary. You have saved $5400 that you want to invest in a certificate of deposit that pays a stated rate (nominal rate) of 4.6%. The interest on this CD is compounded weekly (52 weeks in a year for banking purposes). What is effective rate (annual percentage rate, APY)? (Hint: The effect rate should be greater than the nominal rate.) Show work

Answer 1

Solution:

Effective annual interest rate or annual percentage rate, APY is calculated using the following formula:

EAR or APY = ( 1 + ( r/n) )ⁿ – 1

Where r = nominal Interest rate

n = Number of compounding periods

As per the Information given in the question we have

r = 4.6 % = 0.046   ; n = 52 weeks

Applying the above information in the formula we have

= ( 1 + ( 0.046 / 52) )⁵² – 1

= ( 1 + 0.00088462 )⁵² – 1

= ( 1.00088462 )⁵² – 1

= 1.04705337 – 1

= 0.04705337

= 4.705337 %

= 4.71 % ( When rounded off to two decimal places )

Thus the Effective annual interest rate or annual percentage rate, APY of the Certificate of Deposit = 4.71 %

Note : ( 1.00088462 ) ⁵² is calculated using the excel formula

=POWER(Number,Power) = POWER(1.00088462,52) = 1.04705337