Compound Interest means that you earn "interest on your interest", while Simple Interest means that you don't - your interest payments stay constant, at a fixed percentage of the original principal. First, a calculator to let you see the difference.
The lesson is that compound interest is a better investment, which seems both obvious and moot - after all, bank accounts always pay compound interest anyway. Even a bond investment is really compound interest if you think about it: you get fixed coupons [that's simple interest] but you can invest them to get interest on them [ergo compound interest].
The situation where simple interest occurs naturally is when the principal doesn't change over time. This is true with an interest-only mortgage, for example, where your monthly payments only pay the interest on your loan, but don't pay down the loan itself.
Simple Interest Formula
Lets say that P is your starting principal [spelled -pal and not -ple, because Your Money is Your Pal], r is the interest rate [expressed as a decimal], and Y is the number of years you invest. Then your future value will be:
P [1 + rY] | [Simple Interest] |
P [1 + r]Y | [Annually Compounded Interest] |
Note the two formulas give the same answer for one year. After that, compound interest takes off.
This present value calculator can be used to calculate the present value of a certain amount of money in the future or periodical annuity payments.
Present Value of Future Money
ResultsPresent Value: $558.39 Total Interest: $441.61 |
Present Value of Periodical Deposits
ResultsPresent Value: $736.01
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Balance Accumulation Graph
Schedule
start principal | start balance | interest | end balance | end principal | |
1 | $0.00 | $0.00 | $0.00 | $100.00 | $100.00 |
2 | $100.00 | $100.00 | $6.00 | $206.00 | $200.00 |
3 | $200.00 | $206.00 | $12.36 | $318.36 | $300.00 |
4 | $300.00 | $318.36 | $19.10 | $437.46 | $400.00 |
5 | $400.00 | $437.46 | $26.25 | $563.71 | $500.00 |
6 | $500.00 | $563.71 | $33.82 | $697.53 | $600.00 |
7 | $600.00 | $697.53 | $41.85 | $839.38 | $700.00 |
8 | $700.00 | $839.38 | $50.36 | $989.75 | $800.00 |
9 | $800.00 | $989.75 | $59.38 | $1,149.13 | $900.00 |
10 | $900.00 | $1,149.13 | $68.95 | $1,318.08 | $1,000.00 |
Present Value
Present Value, or PV, is defined as the value in the present of a sum of money, in contrast to a different value it will have in the future due to it being invested and compound at a certain rate.
Net Present Value
A popular concept in finance is the idea of net present value, more commonly known as NPV. It is important to make the distinction between PV and NPV; while the former is usually associated with learning broad financial concepts and financial calculators, the latter generally has more practical uses in everyday life. NPV is a common metric used in financial analysis and accounting; examples include the calculation of capital expenditure or depreciation. The difference between the two is that while PV represents the present value of a sum of money or cash flow, NPV represents the net of all cash inflows and all cash outflows, similar to how the net income of a business after revenue and expenses, or how net benefit is found after evaluating the pros and cons to doing something. The inclusion of the word 'net' denotes the combination of positive and negative values for a figure.
The Time Value of Money
PV [along with FV, I/Y, N, and PMT] is an important element in the time value of money, which forms the backbone of finance. There can be no such things as mortgages, auto loans, or credit cards without PV.
To learn more about or do calculations on future value instead, feel free to pop on over to our Future Value Calculator. For a brief, educational introduction to finance and the time value of money, please visit our Finance Calculator.