This chapter has introduced a number of formulas to calculate simple and compound interest.
The following tables gives the formulas and functions that provide the relationships between the sum invested,PV; the future return, FV; the rate of interest I%, over n, the number of compounding periods.
To calculate
Formula
Spreadsheet Function
Simple interest
FV (Return)
= PV*(1+n*I)
N/A
I% (Rate)
=((FV/PV)-1)/n
N/A
n periods
=((FV/PV)-1)/I
N/A
PV (Investment)
=FV/(1+n*I)
N/A
Compound interest
FV (Return)
=PV*(1+I)^n
=FV(I,n,0,-PV)
I% (Rate)
=(FV/PV)^(1/n)-1
=RATE(n,0,-PV,FV)
n
periods
=ln(FV/PV)/ln(1+I)
=NPER(I,0,-PV,FV)
PV
(Investment)
=FV*(1+I)^-n
=PV(I,n,0,FV)
Key points
Interest is a percentage rate and its specification involves a percentage and a time period.
Simple interest is where the interest earned or owed is not added to the sum invested or borrowed and so doesn’t affect the period interest calculation.
For simple interest FV=PV*(1+n*I%) where FV is the Future Value, PV is the Present value, I% the interest rate and n is the number of interest bearing periods.
To convert from an annual rate of interest to a monthly rate simply divide by 12. Conversions between rates over other periods follow a similar method.
Compound interest is where the interest earned or owed is added to the sum invested or borrowed and so does affect the subsequent interest calculations.
Spreadsheets have a range of financial functions which can be used to simplify the raw formulas involved in interest calculations.
Inflation is an application of compound interest that reduces rather than increases the value of money.
Spreadsheets take the hard work out of calculations, but you still need to know how to do them. Financial Functions with a spreadsheet is all about understanding and reasoning, using a spreadsheet to do the actual calculation.
Understanding Percentages Percentages are something familiar to us all - but they present many pitfalls that need to be avoided.
Interest Simple and Compound We explore the idea of borrowing money for a specified rate of interest or earning interest on an investment. The ideas of Present and Future Value PV and FV are introduced.
Effective Interest Rates We explore the idea of the `effective’ annual interest rate and then on to the Effective Interest Rate/Annual Percentage Rate, the much quoted EIR or APR.
Introduction to Cashflow - Savings Plans In the first of three chapters covering the way in which interest rate affects cashflow we explore savings - but first we introduce some general ideas that apply equally to annuities and repayment loans.
Cashflow Continued - Annuities We move on to annuities in the second of three chapters devoted to exploring the way in which interest rate affects
Exploring Repayment Loans Repayment loans are the subject of the last of three chapters which look at the effects of regular cashflows.
Present and Future Values The principles of present and future value apply even if the cash flow is irregular. The calculations are just a matter of breaking down the cash flow calculations into simple steps.
Investment Analysis How is it possible to evaluate investments that generate irregular cashflows? We explore how NPV can be used to make investment decisions.
Advanced Investment Analysis IRR and MIRR The IRR is perhaps the most complicated of the measures of the value of an investment with an irregular cash flow. Understanding exactly what it means is a good step toward making correct use of it.
