# Continuous Compound Interest Calculator

Initial Investment (P) =   \$

Interest Rate (r) =   %

Time (t) =   years

Total Amount of Money =    \$

** Enter percentages as whole numbers, i.e. 5% should be input as 5. The calculator converts percentages to decimal form.

### Continuous Compound Interest Formula

To solve a problem seeking continuous compound interest, the formula is:

A = Pert

where,
A = Amount of future value
P = Initial amount invested
e = Stands for Napier's number and is approximately 2.7183
r = Interest rate
t = Length of time investment will accrue

### Sample Continuous Compound Interest Problem

Alex has \$7000 to invest in a bank savings account. The savings will accrue interest continuously at 5.7%, how much will he have after 7 years?

A = \$7,000 * 2.7183 .057 * 7

He will have \$10,432.33 after his money has continuously compounded over 7 years.

Keeping in mind this is a theoretical concept as money generally accrues interest monthly, quarterly, semi-annually, or annually... The value in continuous compounding interest is really conveyed when looking at how an investment grows over time. For example if you invest \$10,000 in an S&P fund, which sees an average return of about 10% a year (when looking at the past 90 years) your money almost triples in 10 years with a value of ~\$27,000, but if you let it sit for 30 years you will have just over \$200,000!! This sharp increase over a fairly short period of time illustrates the power of exponential growth (of money). The growth is even more significant as you make contributions over time.

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