Question 1149651
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Learn the loan formula and how to use it....<br>
{{{P = A*((1-(1+r/n)^(-(n*t)))/(r/n))}}}<br>
P = principal (amount of loan)
A = amount of regular payment
r = annual interest rate
n = # of payments per year
t = time (years)<br>
Note from those definitions that r/n is the periodic interest rate, and n*t is the total number of payments.<br>
In this example....<br
{{{13000 = 400*((1-(1+.0425/12)^(-(12*t)))/(.0425/12))}}}<br>
The unknown (number of years to repay the loan, t) is in an exponent; so an algebraic solution will require the use of logarithms.<br>
{{{(13000*(.0425/12))/400 = 1-(1+.0425/12)^(-(12*t))}}}<br>
{{{1-(13000*(.0425/12))/400 = (1+.0425/12)^(-(12*t))}}}<br>
log({{{1-(13000*(.0425/12))/400}}}) = -12t*log({{{(1+.0425/12)}}})<br>
-12t = (log({{{1-(13000*(.0425/12))/400}}}))/log({{{(1+.0425/12)}}})<br>