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?

1 Answer
Jun 17, 2017

Answer:

(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#)