Question #269004

If interest rate is unknown, give the formula for annual interest rate, j.

1
Expert's answer
2021-11-23T17:23:03-0500

We have two cases below

  1. Simple interest

A=P(1+jn)A=P(1+jn)

where AA is the accumulated amount, PP is the principal amount, jj is interest rate and nn is the time period.

We can make jj subject of the formula to get the unknown interest rate jj as follows

A=P(1+jn)A=P(1+jn)


A=P+PjnA=P+Pjn


P+Pjn=AP+Pjn=A


Pjn=APPjn=A-P


PjnPn=APPn{Pjn\over Pn}={A-P\over Pn}


j=APPn\therefore j={A-P\over Pn}


2.Compound interest

A=P(1+j)nA=P(1+j)^n

P(1+j)n=AP(1+j)^n=A

P(1+j)nP=AP{P(1+j)^n\over P}={A\over P}

(1+j)n=AP(1+j)^n={A\over P}

(n1+j)n=nAP(n\sqrt{1+j})^n=n\sqrt{{A\over P}}

1+j=nAP1+j=n\sqrt{{A\over P}}

j=nAP1\therefore j=n\sqrt{{A\over P}}-1



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