Answer to Question #173654 in Financial Math for Easton Ediger

Question

Kevin used his credit card to pay $2544 for a holiday. The interest rate is 18.75 compounded daily. Kevin plans too make a monthly payment of $200.

when will kevin have paid off the Balance in full?

Answer 1

As Kevin plans to make a monthly payment, a month is the period for calculations.

Present value PV = $2544

Periodic payment PMT = $200

Rate of interest per period

$i = \frac{18.75}{12}\%=1.5625 \% = 0.015625 PV = PMT( \frac{1-(1+i)^{-n}}{i} ) \\ 2544 = 200( \frac{1-(1+0.015625)^{-n}}{0.015625} ) \\ 1-(1.015625)^{-n} = 0.19875 \\ (1.015625)^{-n} = 1-0.19875 \\ (1.015625)^{-n} = 0.80125$

Taking logarithm of both sides, we get

$-nlog1.015625=log0.80125 \\ n = -\frac{log0.80125}{log1.015625} \\ n = 14.29$

Answer: 14 months and 9 days.