INTEREST RATES: Something to factor in

I wanted to comment on Andy Obermueller’s article on interest rates in the Aug. 10 Coeur Voice section of the paper.

Several definitions were given, but there was never a discussion about simple vs. compound interest. Depending on the number of compounding periods per year, the effective interest rate can increase by a considerable amount. This can be a large impact to investing money, as well as borrowing money.

We can compute amount A after t years with the following:

A = P(1 + r/n)^nt

Where:

P = principal amount

r = rate of interest

n = compounding periods

t = time in years

For example, if the compounding period is annually (n=1), we start with $100000 (P=$100000), the interest rate is 5% (r=0.05), and this is over 1 year (t=1):

A = P(1 + r/n)^nt

A = $100000(1 + 0.05/1)^(1*1)

A = $100000(1.05)^1

A = $100000(1.05) = $105000.00

$5000.00 interest gained for 1 year.

But if the compounding period is monthly, we have:

A = P(1 + r/n)^nt

A = $100000(1 + 0.05/12)^(12*1)

A = $100000(1.004166)^12

A = $100000(1.0511618) = $105116.18

$5116.18 interest gained for 1 year.

Same calculations for a time of 30 years gives:

Compounding annually:

A = $100000(1 + 0.05/1)^(1*30)

A = $432194.23

$332194.23 interest gained (30 years).

Compounding monthly:

A = $100000(1 + 0.05/12)^(12*30)

A = $446774.43

$346774.43 interest gained (30 years).

The above shows more than a $14,000 difference depending on the number of compounding periods.

I thought readers should be aware of this.

DAVID GRADIN

Rathdrum