Question

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

(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?

Answer 1

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

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

Explanation:

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`)