An amount of $AUD500$ is invested in a bank at compound interest?

Question

(a) at $6%$ p.a. at quarterly rests for $3$ years, then what is the interest earned?
(b) In another bank, the interest received is same but at an annually compounding rate, then what is the interest rate paid?

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Answer 1 · 2017-06-17T05:21:48

(a) Interest earned is $AUD$ $97.81$

(b) Second bank offers $6.14%$ p.a.

If an amount $P$ is invested at a simple rate of interest $r$ for a period of $t$ years

the total amount becomes $P(1+r/100)^t$ , if interest is compounded annually.

if it is compounded more frequently, say $n$ times in a year, the amount becomes $P(1+r/(100xxn))^(nxxt)$

As here, interest is compounded quarterly at $6%$ amount
of $AUD500$ in three years becomes

$500(1+6/(100xx4))^(4xx3)=500xx1.015^12$

= $500xx1.19562=AUD" "597.81$ i.e. interest is $AUD$ $97.81$

Now let us say he earns a rate of $r_2%$ p.a. in second bank, compounded annually.

Then as the amount would be $597.81AUD$ , we have

$500xx(1+r_2/100)^3=597.81$

or $(1+r_2/100)^3=597.81/500=1.19562$

or $1+r_2/100=root(3)1.19562=1.061364$

and $r_2=0.061364xx100=6.14%$ p.a. (upto $2dp$ )