Question

A bank pays interest at `6%` per annum when invested for `3` years compounded quarterly. What is the amount of interest paid by the bank. If second bank pays interest compounded annually and pays the same interest, what is interest rate paid by it?

Answer 1

(a) `AUD97.81` and (b) Interest rate is `6.14%` up to 2dp.

Explanation:

An amount `P` deposited for `n` quarters at an anuual rate of interest of `r%` (i.e. quarterly interest rate of `r/4%`) compounded quarterly becomes `P(1+r/(4xx100))^n`

(a) Hence an amount of `P` at `6%` per annum after `3` years becomes

`P(1+6/400)^12=Pxx1.015^12=Pxx1.19562`

and hence interest earned is `1.19562P-P=0.19562P`

Here amount is not mentioned, but say it is `AUD500`, then interest earned is `AUD500xx0.19562=AUD97.81`

(b) If Marcus earns same interest i.e. `AUD97.81` on `AUD500` in second bank where interest is compounded annually say at `r%`,

then `500(1+r/100)^3=597.81`

and `(1+ r/100)^3=597.81/500=1.19562`

or `1+r/100=root(3)1.19562=1.061364`

i.e. `r/100=0.061364` and `r=6.1364%~=6.14%`