The Equations

How are the financial calculations in the app made? Well, first of all, the calculations in the app are based upon what we call "end of period" payments. That means we accrue interest , on investments, or pay interest, on loans and credit cards, at the end of the period. For example, this would calculate your loan payment on a car based upon you making your payment at the end of the month, not the beginning of the month. There are separate equations you can use for beginning of the period but they provide a slightly different outcome than the ones in this app's end of period calculations.

The equations use the following variables:

S = Future Value of the Investment

P = Present Value of the Investment

R = Regular Payment or Investment Amounts, for example, a monthly payment or investment amount.

N = Time Period for the investment. You will enter time as years in the app. For example, if your time period is 1 year 9 months, you would enter 1.75 years.

i = Interest Rate or Rate of Return. You will enter your value as a percent. The app will then automatically change that percent to a decimal, ie, when you enter 5 for 5%, the app will change it to .05 for you.

The interest rates you will enter will be annual rates, sometimes referred to as APR. Time will be in years. If you are calculating a different time interval, monthly payments for example, the app will automatically divide the annual interest rate by 12 and multiply the time period by 12. You won't have to worry about this. Simply enter time in years and interest as an annual %. Watch the parentheses and order of operations when using these equations.

Simple Interest

Calculate simple interest on principal. Do not add the interest to the principle.

S = ( 1 + N i)

Compound Interest

Calculate simple interest on principal. Add the interest to the principle each time. Your principal grows each time interest is added.

S = ( 1 + i) N

Equal Payment Compound Amount

If you invest $R for N years at interest rate i%, how much money ($S) would you have at the end of those N years.

S = R ( ( 1 + i) N - 1 ) / i

Single Payment Present Worth

How much should I deposit now ($P) to be worth a future amount of $S if invested for N years at i%

P = S / ( 1 + i) N

Equal Payment Present Worth

How much money would I need now ($P) to make n payments of $R each if the remaining funds remained invested at i% rate of return.

S = R ( ( 1 + i) N - 1 ) / ( i ( 1 + i) N )

Equal Payment Sinking Fund

What $R must be regularly deposited for N time intervals to be worth $S at the end of those N time periods when the rate of return for the investment is i%

R = S ( i ) / ( ( 1 + i) N - 1 )

Equal Payment Capital Recovery (Loan Payments)

What regular payments ($R) can be made N times from a starting fund of $P when the remaining funds are invested at i%.

R = P ( i ( 1 + i) N ) / ( ( 1 + i) N - 1 )

Credit Card Payoff

How many years will it take to payoff a credit card balance ($P) based upon your card's annual percentage rate (i%), and the amount you plan to pay monthly ($R). (Of course this assumes you make no new charges on the card) (Note that ln stand for natural log)

N = -1/3 ln (1 + P/R (1 - ( 1 + i) 30 ) / ln ( 1 + i) / 12

Compound Annual Growth Rate (CAGR)

What was the average rate of return (i%) on an investment with a beginning value of $P and an ending value of $S after N years.

CAGR = (S / P) 1/N - 1

Rule of 72

How many years (N) would it take for your investment to double with an i% annual rate of return.

N = 72 / i