Calculating duration of a loan

Question

How do I calculate the number of periods of a loan given the starting balance, the annual percentage rate, and the monthly payment amount?

I know how to calculate the monthly payment amount given the first two, plus the number of periods.

You solve the same equation for the number of periods. It involves taking a logarithm because the number of periods is in an exponent. — Ross Millikan, Jan 17 '17 at 16:47

score 1 · Accepted Answer · answered Jan 17 '17 at 16:56

1

$B = \sum_\limits {i=1}^n \frac {CF_i}{(1+r)^n}$ is your NPV calculation. The NPV of the future cash flows equals the loan balance.

When the cash flows are uniform, the expression can be simplified to: $B = P \frac {(1+r)((1+r)^n-1)}{r}$ Now solve for $n.$

$1+\frac {Br}{P(1+r)} = (1+r)^n\\ \dfrac {\log \left(1+\frac {Br}{P(1+r)} \right)}{\log (1+r)} = n$

answered Jan 17 '17 at 16:56

Doug M

Thanks. I think I derived the same formula, only not as far simplified. – Ralph Jan 17 '17 at 16:59

1 Answers1