Math CentralQuandaries & Queries


Question from Carolyn:

If I invested $1000.00 (one time ) at 1% compounded daily, how long would it take to have $100,000?

Beware Carolyn.

"Daily compounded interest" is not given at the daily rate, but rather the annualized rate. This is a key technique for people to scam money out of unsuspecting victims.

The formula for compounded interest is simply this:

B = P(1+R)N

Where B is the final balance, P is the principal, R is the rate (1% = 0.01) of interest paid per compounding period and N is the number of compounding periods.

If you were actually to be paid 1% interest each day, then you can answer the question this way:

100 000 = 1 000(1 + 0.01)N

which you can solve easily with logarithms:

100 = (1.01)N

log 100 = N log 1.01

N = log 100 / log 1.01

N = 463 days, about 1 year and 3 months.

However, that is what scammers want trusting people to believe. In fact, when daily compounded interest is quoted by any respectable financial institution, it may be in the range of 1% to 10% typically, but it applies to the annualized rate (that is, this percentage is actually 365 times the daily rate).

So actually, you would calculate the number of compounding periods with the same formula, but R is 0.01/365:

B = P(1+R)N

100 000 = 1 000 (1 + 0.01/365)N
100 = (1.000027397)N
N = log 100 / log 1.000027397

N = 168 091 days, more than 460 years!!

Be very very careful if entering into any financial arrangement with someone actually offering a percentage that is paid daily. If it sounds too good to be true, it almost certainly is.

Stephen La Rocque.>

About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS