Question

Daisy purchases 10,000 tennis balls for $4200 she uses her credit card which has an interest rate of 14% if she makes a monthly payment of $200 how many months will it take Daisy to pay off her purchase?

Answer 1

25 months

Explanation:

We can use the amortization formula to solve for t.

That formula tells you the monthly payment as a function of interest rate (r=.14), compounding periods per year (n=12), principal borrowed (P=4200), and number of years (t). Using the given values, we have ...

200 = 4200(r/n)/(1 -(1 +r/n)^(-nt))

1 -(1 +r/n)^(-nt) = 4200(r/n)/200

1 -21r/n = (1 +r/n)^(-nt)

log(1 -21r/n) = -nt·log(1 +r/n)

-log(1 -21r/n)/log(1 +r/n) = nt . . . . . . the number of months we want

-log(1 -21(0.14)/12)/log(1 +0.14/12) = nt = 24.23

It will take Daisy about 25 months to pay of her credit card.