# First Simple Bank pays 9.9 percent simple interest on its investment accounts. If First Complex...

## Question:

Two banks, First Simple Bank and First Complex Bank, are desirous of attracting deposits by offering investment accounts. First Simple pays interest at a rate of 9.9 percent calculated using simple interest on its investment accounts. First Complex pays compound interest, annually, on its accounts. For an investment horizon of 10 years, what rate would First Complex Bank need to pay on its investment accounts to match or equal the investment made with First Simple Bank?

## Simple Interest and Compound Interest

One way banks finance their operations is through deposit accounts. These accounts can be interest bearing, which means the principal amount in the account earns interest at regular intervals. This interest earned can either be simple interest or compound interest. With simple interest bearing accounts, interest is calculated (and paid) on the original principal amount every time interest is to be paid. For compound interest bearing accounts however, interest is calculated (and paid) on the original principal for the initial time period, only. This interest is then added to the original principal and a new principal amount is set for the next interest payment period. This new principal, i.e. beginning principal plus interest earn this period, is used to calculate the interest amount for the next period. Using compound interest, the interest earned in each period also earns interest in the next period hence compounding the effect.

`First, let's calculate the interest to be earned over the 10 year investment horizon at 9.9 percent simple interest at First Simple Bank. For...

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