Simple InterestSimple InterestIn simple interest, only the original principal bears interest and the interest to be paid varies directly with time.The formula for simple interest is given byI=PrtThe future amount isF=P+IF=P+PrtF=P(1+rt)WhereI = interestP = principal, present amount, capitalF = future amount, maturity valuer = rate of simple interest expressed in decimal formt = time in years, term in yearsOrdinary and Exact Simple InterestIn an instance when the time t is given in number of days, the fractional part of the year will be computed with a denominator of 360 or 365 or 366. With ordinary simple interest, the denominator is 360 and in exact simple interest, the denominator is either 365 or 366. We can therefore conclude that ordinary interest is greater than exact interest.Note:When simple interest (ordinary or exact) is not specified in any problem, it is assumed as ordinary.Ordinary simple interest is computed on the basis of bankers year.Bankers year1 year = 12 months1 month = 30 days (all months)1 year = 360 daysExact simple interest is based on the actual number of days in a year. One year is equivalent to 365 days for ordinary year and 366 days for leap year. A leap year is when the month of February is 29 days, and ordinary year when February is only 28 days. Leap year occurs every four years.Note:Leap years are those which are exactly divisible by 4 except century years, but those century years that are exactly divisible by 400 are also leap years.If d is the number of days, then ...In ordinary simple interest t=d360In exact simple interest t=d365 (for ordinary year) t=d366 (for leap year)ompound InterestSPONSORED LINKSIn compound interest, the interest earned by the principal at the end of each interest period (compounding period) is added to the principal. The sum (principal + interest) will earn another interest in the next compounding period.Consider $1000 invested in an account of 10% per year for 3 years. The figures below shows the contrast between simple interest and compound interest.At 10% simple interest, the $1000 investment amounted to $1300 after 3 years. Only the principal earns interest which is $100 per year.

At 10% compounded yearly, the $1000 initial investment amounted to $1331 after 3 years. The interest also earns an interest.

Elements of Compound InterestP = principal, present amountF = future amount, compound amounti = interest rate per compounding periodr = nominal annual interest raten = total number of compounding in t yearst = number of yearsm = number of compounding per yeari=rm and n=mtFuture amount,F=P(1+i)n or F=P(1+rm)mtThe factor (1+i)n is called single-payment compound-amount factor and is denoted by (F/P,i,n).Present amount,P=F(1+i)nThe factor 1(1+i)n is called single-payment present-worth factor and is denoted by (P/F,i,n).Number of compounding periods,n=ln(F/P)ln(1+i)Interest rate per compounding period,i=FPn1Values of i and nIn most problems, the number of years t and the number of compounding periods per year m are given. The example below shows the value of i and n.ExampleNumber of years, t=5yearsNominal rate, r=18% Compounded annually (m=1) n=1(5)=5i=0.18/1=0.18 Compounded semi-annually (m=2) n=2(5)=10i=0.18/2=0.09 Compounded quarterly (m=4) n=4(5)=20i=0.18/4=0.045 Compounded semi-quarterly (m=8) n=8(5)=40i=0.18/4=0.0225 Compounded monthly (m=12) n=12(5)=60i=0.18/12=0.015 Compounded bi-monthly (m=6) n=6(5)=30i=0.18/6=0.03 Compounded daily (m=360) n=360(5)=1800i=0.18/360=0.0005Continuous Compounding (m )In continuous compounding, the number of interest periods per year approaches infinity. From the equationF=(1+rm)mtwhen m, mt=, and rm0. Hence,F=Plimm(1+rm)mtLet x=rm. When m, x0, and m=rx.F=Plimx0(1+x)rxtF=Plimx0(1+x)1xrtFrom Calculus, limx(1+x)1/x=e, thus,F=Pert