Hi Tonya,

(Please ignore my comment above. It seems I saved and posted it before I was finished.)

Your instructor is correct. Now let's figure out why by calculating A, using your formula and the following assumptions:

Your initial account balance (P) = $1,000. The account earns an annual rate of 5% (r = .05), which is compounded quarterly (m = 4). Assume further that you wish to know the account balance after 2 years, so the number of compounding periods (n) = 8.

Using your formula, as written above, the calculation is as follows:

A = P * ((1 + (r * m))^n

A = $1,000 * (1 + (.05 * 4))^8

A = $1,000 * (1 + .2)^8

A = $1,000 * 4.3

A = $4,300

Would an account with an initial balance of $1,000 grow to $4,300 after 2 years, given interest of 5% per year? Not likely, when (ignoring the effect of quarterly compounding for the moment) we know that the account will earn $50 in year 1 ($1,000 * 5%) and $52.50 in year 2 ($1,050 x 5%). Consequently, the account balance at the end of year 2 (compound annually - as opposed to quarterly - for simplicity) would be $1,102.50 ($1,000 + $50 + $52.50). $1,102.50 vs. $4,300? Something must be wrong.

Can you see where the problem is? Here's a hint: As written, your formula multiplies the initial deposit of $1,000 by 1.2 (1 + (.05 * 4) = 1.2) to the 8th power. This would suggest that the quarterly interest rate - compounded for 8 quarters - is equal to 20%. We know that the *quarterly* interest rate cannot be higher than the
*annual* rate, let alone 4 times higher. Is it any wonder the calculated balance of $4,300 is so large?

How can you tweak your formula ever so slightly to convert the annual rate of 5% to the correct quarterly rate, which we know cannot be 20%?

Once the formula is revised, the ending balance in the account after two years will be $1,104.49.

I look forward to hearing your thought process and conclusion.

Jeff

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