please help!!

Question

A contract requires end-of-month payments of $180 for another 9 1/4 years. What would an investor pay to purchase this contract if she requires a rate of return of 3.6% compounded monthly? (Round your answer to 2 decimal places.)

Answer 1

Hi Maliha,

 

Let's begin by writing the Compound Interest formula and identifying its variables and its values given in our problem:

    F = P(1 + r/p)^(t)(p)  [Compound Interest formula]

    F (future amount) = (180)(9.25)(12) = $19,980

    P (principal, initial amount) = unknown

    r (annual interest rate) = 3.6% = 3.6/100 = 0.036

    p (periods per year) = 12 [compounded monthly]

    t = years

 

Now let's plug in all our known values and solve for our unknown(P):

    19,980 = P(1 + 0.036/12)^(9.25)(12)

    19,980 = P(1 + 0.003)¹¹¹

    19,980 = P(1.003)¹¹¹

    19,980 = P(1.394451986)

    P = 19,980/1.394451986

    P = 14,328.20936

    P = $14,328.21

            (rounded to nearest hundredth)

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.