find the present value on Php 7,896 for 4 months of a simple interet rate of 7 1/2%.

Question

formula is F=P+(I+rt), means F=principal + (interest+rate*time).

 

Answer 1

Simple interest, which is the interest computed on the original principal only, is defined by the following formula:     I = Prt   ,

     where P is the principal (or present value), r is the interest rate, and t is the time (in year)

The future value (or accumulated amount), which is the sum of the principal and interest after t years, is given by the following formula:

     F = P + I

Substituting 'Prt' for 'I' in the above formula, we arrive at the following:

     F = P + Prt

Factoring out 'P' from both terms on the right hand side of the equation, we get:

     F = P(1 + rt)

Since we are looking to solve for the present value (P), we first solve the equation above for P by dividing both sides of the equation by '1 + rt':

     F/(1 + rt) = P(1 + rt)/(1 + rt)

     F/(1 + rt) = P

I'm assuming the future value is $7,896   ==>   F = 7896

At a rate of 7.5%   ==>   7.5%/100% = 0.075

For 4 months   ==>   4 months/12 months per year = 0.333

Plug in these values into the equation solved for P to solve for the present value:

     P = F/(1 + rt)

        = 7896/(1 + 0.075·0.333) 

        = 7896/(1 + 0.025)

        = 7896/1.025

        = 7703.41

Thus, the principal (or present value) is $7,703.41