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# how do i calculate nominal interest rate compounded half yearly with no rate given. answer must be in % and correct to two decimal places.

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how do i calculate nominal interest rate compounded half yearly with no rate given. answer must be in % and correct to two decimal places.

Jan 10, 2019

#1
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FV = PV(1+ int/2)^(yr*2)     interest = YEARLY interest       Divided by two to find interest per PERIOD (twice per year)

yr*2 = number of periods       = # years * 2 times per year

FV = future value     PV = present value (or initial deposit)

Jan 10, 2019
#2
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We have that

A = P ( 1 + r/2)^(2n)

Assuming that we know

A= the final amt

P = amt invested

n = number of years of compounding

We can find r = the interest rate thusly :

Divide both sides by P

(A/P)  = (1 + r/2)^(2n)       take each side to the 1/ [2n]  power

(A/P)^(1/ [ 2n] )  =   [ (1 + r/2)^(2n) ]^(1/ [2n] )

(A / P) ^(1 / [2n] )    =   1 + r/2          subtract 1 from both sides

( A / P)^(1/ [2n ] )  - 1  =  r / 2          multiply both sides by 2

2 (A / P)^(1 / [2n]) -  2     =  r   Jan 10, 2019
#3
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...adding to Chris answer:      r will de the interest in DECIMAL form......multiply by 100 to get annual percentage.

ElectricPavlov  Jan 10, 2019
#4
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Thanks, guest.....!!!!   CPhill  Jan 10, 2019