Question

A career counselor decides to make monthly payments of $150 on credit card debt of $3489.64 and discontinue using the credit card.

1. Assuming the annual interest rate is 22.2%, how many months will it take her to repay the debt? Round to the next month.
2. How many fewer months would it take to repay the debt if the counselor makes monthly payments of $200.  Round to the next month.

Answer 1

a

PVOrdinary Annuity = C*[(1-(1+i/(f*100))^(-n*f))/(i/(f*100))]

C = Cash flow per period

i = interest rate

n = number of payments I f = frequency of payment

3489.64= 150*((1-(1+ 22.2/1200)^(-n*12))/(22.2/1200))

n(in years) = 2.56

Using Calculator: press buttons "2ND"+"FV" then assign

PV =-3489.64

PMT =150

I/Y =22.2/12

FV = 0

CPT N

Number of years = N/12

Using Excel

=NPER(rate,pmt,pv,fv,type)/no. of payments per year

=NPER(22.2/(12*100),-150,,3489.64,)/12

Number of months = years*12 = 2.56*12 = 31 months

b

PVOrdinary Annuity = C*[(1-(1+i/(f*100))^(-n*f))/(i/(f*100))]

C = Cash flow per period

i = interest rate

n = number of payments I f = frequency of payment

3489.64= 200*((1-(1+ 22.2/1200)^(-n*12))/(22.2/1200))

n(in years) = 1.77

Using Calculator: press buttons "2ND"+"FV" then assign

PV =-3489.64

PMT =200

I/Y =22.2/12

FV = 0

CPT N

Number of years = N/12

Using Excel

=NPER(rate,pmt,pv,fv,type)/no. of payments per year

=NPER(22.2/(12*100),-200,,3489.64,)/12

Fewer months = 30.72-1.77*12 = 10 months