The annual interest rate of Erika's savings account is 6.4%, and simple interest is calculated quarterly. What is the periodic interest rate of Erika's account?

1 Answer
Jan 27, 2018

i=1.6% " per qtr"

Explanation:

The annual interest rate is given at 6.4%. Knowing that 1 " year(yr)=4 quarters(qtr), the quarterly interest rate is calculated as;

I=Pxxixxn, isolate the unknown variable; that is, i
i=(I)/(Pxxn)

where:

I="Interest"
P="Principal"
i="interest rate"
n="number of years"

Multiplying the equation by 1/4 does not alter the value of the annual interest rate given @ 6.4%; i.e.,

i=(I)/(Pxxn)}1/4;

color(red)(i/4)=(I)/(Pxx4n

where:

color(red)(=i/4=0.064/4=0.016=1.6% "per qtr")=" the quarterly interest rate that is equally distributed for a year "

i=(cancel(4)xxI)/(Pxxcancel(4)n)

i=(I)/(Pxxn), the original formula