• Jun 28th 2008, 01:11 AM
slanno
Scott is saving for an overseas holiday and he is looking for the best bank in which to invest his money. Three banks are offering different interest rates as follows:

Bank Able: 8.1%(nominal p.a.) compounded monthly
Nank Beble: 8.2% (nominal p.a.) compounded twice yearly
Bank Ceble: 8.4% (effective p.a.) effective interest rate per year

a) compare effective rates to find which bak offers the best return on investments DONE (Talking)

b) Check your answer to a) by considering the amount of interest earned be each option over a 5 year time period. I used \$5000 as example. DONE (Evilgrin)

c) Scott chooses to invest with bank ceble. Find their quarterly interest rate.

i need help with this one!! how do i find the quarterly interest rate??? (Headbang)

Cheers for the help!!
• Jun 28th 2008, 03:40 AM
Soroban
Hello, slanno!

Quote:

Bank Ceble: 8.4% (effective p.a.) effective interest rate per year

c) Scott chooses to invest with bank Ceble. Find their quarterly interest rate.

Let $r$ = quarterly interest rate.

If he invests $P$ dollars for a year, his final balance is: . $P(1 + r)^4\;\;{\color{blue}[1]}$

Since the effective rate is 8.4%.
. . his final balance is: . $P + 0.084P \:=\:(1.084)P\;\;{\color{blue}[2]}$

Equate [1] and [2]: . $P(1+r)^4 \:=\:(1.084)P \quad\Rightarrow\quad (1+r)^4 \:=\:1.084$

. . . . . . $1 + r \:=\:\sqrt[4]{1.084} \quad\Rightarrow\quad r \:=\:\sqrt[4]{1.084} - 1$

Therefore: . $r \;=\;0.020369152 \;\approx\;2\%$