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Suppose there is a loan with equated monthly installments. If I know the loan period, loan amount and equated monthly installment amount, is there a way to calculate the interest rate?

EMI= a * (1 + r)^p / [(1 + r)^p - 1]

a: loan amount

r: interest rate

p: loan period

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You need to solve for the interest rate. Also your formula should be

EMI = a*r*(1 + r)^p/((1 + r)^p - 1)

Derived from the sum of the discounted payments being equal to the principal

Example solution

a = 1000
p = 3
r = 0.05

∴ EMI = 367.209

Suppose the interest rate is unknown

EMI = 367.209
a = 1000
p = 3

solve for varying r until this equation is satisfied:

Plot of (EMI (1 - (1 + r)^-p))/r - a over a range of r

enter image description here

or use an online solver, e.g.

enter image description here

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