Question

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?

Answer 1

`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