Payment Question

Question

Marilyn was supposed to pay $1590 to Bernice on March 15. Some time later Marilyn paid Bernice an equivalent payment of $1640.83, allowing for a time value of money of 2.7% compounded monthly. When did Marilyn make the payment?

Answer 1

Hi Marilyn,

 

Let's begin by recalling the Compound Interest formula and explaining all its variables:

    A = P(1 + (r/p)^pt

    A = future amount paid

    P = initial amount loaned

    r = annual interest rate

    p = payment periods per year

    t = time in years

 

Now let's plug in all our values as per our problem and solve for 12t (months of loan):

    1640.83 = 1590(1 + 0.027/12)^12t

    (1 + 0.00225)^12t = 1640.83/1590

    (1.00225)^12t = 1.032

    12t(log(1.00225)) = log(1.032)

    12t = log(1.032)/log(1.00225)

    12t = 0.01368/0.000976

    12t = 14.02 months 

 

Since t is in years then 12t is in months and, therefore, we can see that the loan will be paid off in 14 months after March 15, i.e. May 15 of the following year.

 

This problem demonstrated a plug-in and solve exercise using the Compound Interest formula.

 

Thanks for submitting the problem and glad to help.

 

God bless, Jordan.