Solve the following problem. PV=$24,187​; n=102​; i=0.035​; PMT=?​;

Question

Solve the following problem.

PV=$24,187​; n=102​; i=0.035​; PMT=?​;

PMT=$_______ ​(Round to two decimal​ places.)

Answer 1

In Excel, you would just use =PMT(0.035,102,24187). You get $872.66

There may be a similar formula on your calculator.

Your book probably gives you a formula.

Alternatively, you can derive the value using the sum of a geometric series. If you pay P each month, the present value is Prⁿ, where r = 1/(1+i), and the sum is Pr(1 - rⁿ)/(1-r)

Note that r/(1-r) = 1/(1+i)/(1 - 1/(1+i)) = 1/i

Thus, the sum is P(1 - (1/1+i)ⁿ)/i

Then, if our value is the Principal, P = Principal(i)/(1 - (1/1+i)ⁿ)

Then, P = 24187 * .035/(1 - (1/1.035)¹⁰²) = $872.66