The Future Value of Money With Different Compounding Periods

In this post, I will show you the importance of the compounding period in calculating the future value of money.

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The setup for this example is as follows: You have $10,000 deposited in a saving account with a fixed annual interest of 5% for ten years.

The Future Value of Money with Different Compounding Periods


Let's quickly calculate what happens to your money at the end of ten years with annual compounding:

PV = \$10,000
N = 10 \; years
r = 0.05 (5\%)
FV = ?
FV = PV (1 + r)^N
FV = \$10,000 (1 + 0.05)^{10}
FV = \$10,000 (1+ 0.05)^{10}
FV = \$10,000 (1.05)^{10}
FV = \$10,000 \times 1.6289
FV = \$16,288.95

Your $10,000 becomes $16,288.95 in 10 years with a 5% fixed annual interest rate compounded annually.

Now let's look at what happens if the money is compounded in different frequencies. To do that, we need to introduce a modified formula:

r = annual \; interest \; rate
N = number \; of \; years
m = compounding \; periods \; (per \; year)
PV = Present \; Value
FV = Future \; Value
FV = PV(1 + \frac{r}{m})^{m \times N}

Monthly Compounding

N = 10 \; years
r = 0.05 (5\%)
m = 12 \; months
PV = \$10,000
FV = ?
FV = PV(1 + \frac{r}{m})^{m \times N}
FV = \$10,000 (1 + \frac{0.05}{12} )^{12 \times 10}
FV = \$10,000 (1 + 0.00416 )^{120}
FV = \$10,000 (1.00416 )^{120}
FV = \$10,000 \times 1.6457
FV = \$16,456.98

Your $10,000 becomes $16,456.98 in 10 years with a 5% fixed annual interest rate compounded monthly. This (monthly compounding) is larger than the previous case (yearly compounding) by $168.03.

Weekly Compounding

N = 10 \; years
r = 0.05 (5\%)
m = 52 \; weeks
PV = \$10,000
FV = ?
FV = PV(1 + \frac{r}{m})^{m \times N}
FV = \$10,000 (1 + \frac{0.05}{52} )^{52 \times 10}
FV = \$10,000 (1 + 0.000962 )^{520}
FV = \$10,000 (1.000962 )^{520}
FV = \$10,000 \times 1.6487
FV = \$16,487.20

Your $10,000 becomes $16,487.20 in 10 years with a 5% fixed annual interest rate compounded weekly. This (weekly compounding) is larger than the yearly compounding by $198.25 and larger than the monthly compounding by $30.22.

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