   SEARCH HOME Math Central Quandaries & Queries  Question from Kenneth: Hello: Is compound interest on $\$1.00$for one year the same as simple interest on$1.00 for one year? Compound interest would be $\$1.01,$and I believe the same amount would be the same at simple interest. Hi Kenneth, You haven't said what the interest rate is but from your calculations I assume it's 1% per year. You also didn't say how many times per year the interest is compounded but again from your calculations I assume you are compounding once per year. If both my assumptions are correct then yes, the return at the end of a year would be the same as with simple interest. If however you compound twice per year, every six months, the calculation is different. What is the value of$\$1.00$ invested for one year at a rate of 1% per year compounded every six months? For this question, $\$1.00$invested at 1$ per year for six months would yield

$\1.00 + \1.00 \times \frac{0.01}{2} = \1.00\times \left(1+ 0.005\right) = \1.005.$

This amount is then invested at 1% per year for 6 months and would yield

$\1.005 + \1.005 \times \frac{0.01}{2} = \1.005\times \left(1+ 0.005\right) = \1.010025.$

For a general development of the value at the end of $m$ years of $\$p,$invested at a rate of$100 \times r\% = r$per year, compounded$k\$ times per year I suggest you look at my response to Kayla.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.