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
Jarni Renz
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

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