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?

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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?

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Answer 1 · 2018-01-27T09:12:45

$i = 1.6 % per qtr$ $i=1.6% " per qtr"$

Explanation:

The annual interest rate is given at 6.4%. Knowing that $1 y e a r (y r) = 4 q u a r t e r s (q t r)$ $1 " year(yr)=4 quarters(qtr)$ , the quarterly interest rate is calculated as;

$I = P \times i \times n$ $I=Pxxixxn$ , isolate the unknown variable; that is, $i$ $i$
$i = \frac{I}{P \times n}$ $i=(I)/(Pxxn)$

where:

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

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

$i = \frac{I}{P \times n}} \frac{1}{4}$ $i=(I)/(Pxxn)}1/4$ ;

$\frac{i}{4} = \frac{I}{P \times 4 n}$ $color(red)(i/4)=(I)/(Pxx4n$

where:

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

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

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

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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

Explanation:

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