# First Simple Bank pays 9.2% simple interest on its investment accounts. If First Complex Bank...

## Question:

First Simple Bank pays 9.2% simple interest on its investment accounts.

If First Complex Bank pays interest on its accounts compounded annually, what rate should the bank set if it wants to match First Simple Bank over an investment horizon of 8 years?

## Interest

Interest can be defined as fee or charge paid by a borrower or deposit taker for borrowing or depositing money to the lender or depositor.

Interest can be simple interest or compound interest. Difference between simple and compound interest is that in compound interest, interest is also paid on accumulated interest of earlier periods.

First Simple Bank

Simple Interest = {eq}P*R*T/100 {/eq}

Where,

P= Principal amount

R= Rate of interest = 9.2%

T= Time Period= 8 years

Let us assume principal be Rs. 100

Simple Interest = (100*9.2*8)/100

=73.6

Now, we need to find the rate of interest at which First complex bank will pay 73.6 as interest on the same principal and same time.

Compound Interest (C) = {eq}P[(1+r)^n-1] {/eq}

where,

P = Principal amount

r= interest rate

n = time period

{eq}73.6 = 100[(1+r)^8-1] {/eq}

{eq}0.736=(1+r)^8-1 {/eq}

{eq}1.736 = (1+r)^8 {/eq}

{eq}1.736^{1/8}= 1+r {/eq}

1.07138=1+r

r= 0.07138 = 7.14% 