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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.

Guest Jan 10, 2019

#1**+2 **

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)

ElectricPavlov Jan 10, 2019

#2**+1 **

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

CPhill Jan 10, 2019

#3**+1 **

...adding to Chris answer: r will de the interest in DECIMAL form......multiply by 100 to get annual percentage.

ElectricPavlov
Jan 10, 2019