simple interest

Suppose a bank account is opened at time 0 and M0 is deposited into the account. A simple interest is interest with the following characteristics:

  1. 1.

    it is earned at subsequent time periods t,2t,, where t is the length of the initial time interval (1 for 1 month, 12 for 1 year, etc…)

  2. 2.

    the interest earned at the end of each time period is the same regardless of the time period

The following table illustrates the structure of the simple interest.

time period at principal interest interest accrued
0 M0 0 0
t M0 i i
2t M0 i 2i
3t M0 i 3i
nt M0 i ni

The``total′′interesti(nt)earned(accrued)attheendoftimentisni.Iftheaccountisclosedandthemoneywithdrawnattheendofnt,andthetotalamountofmoneyreceivedisM(nt)=M0+ni.Theinterestrateassociatedwiththesimpleinterestaspresentedabovebetweentwotimeperiods,sayatandbt,isgivenbyr(at,bt)=1M0i(bt)-i(at)bt-at=iM0t,whichdoesnotdependonthechoiceofaandb.Inotherwords,theoriginalprincipalM_0,theamountofinteresti,andthelengthoftheinitialtimeintervaltareenoughtodeterminetheinterestrate.𝐑𝐞𝐦𝐚𝐫𝐤. • The expression for the effective interest rate for simple interest is a bit more complicated: eff.r(at,bt)= 1 M(at) i(bt)-i(at) bt-at = 1 M 0 +ai i t , which decreases with increasing a . Imagine as a becomes very large, the increase in interest has practically no impact on the “accumulated” principal ⁢ M ( ⁢ a t ) . • More generally, we say that an interest is simple if its interest rate r is constant with respect to time t . Solving r= 1 M 0 i(t)-i(0) t-0 for ⁢ i ( t ) , we get = ⁢ i ( t ) ⁢ M 0 r t , or that the accrued interest is a linear function of t . It grows directly proportionally with respect to time. Titlesimple interestCanonical nameSimpleInterestDate of creation2013-03-22 16:40:06Last modified on2013-03-22 16:40:06OwnerCWoo (3771)Last modified byCWoo (3771)Numerical id7AuthorCWoo (3771)Entry typeExampleClassificationmsc 00A06Classificationmsc 00A69Classificationmsc 91B28Related topicCompoundInterestRelated topicInterestRate