| Special Assignment Game 4 - Off-season Break
Mid Semester Break Pracalculus 64181 - Introduction to Exponentials 4.1 #11 Expanded Solution - To Be Discussed in Class |
4.1 #11 Credit card balanced owed is $2000, monthly interest rate
is 1.5 %,
and monthly minimum payment is 2.5 %. Before the end of each month
(a) Use a table showing minimum payment and interest to show balance through end of 12 months:
| Month, t | Balance, $, Bt
Bt = B0 (0.99)t |
Interest, $, It
It = Bt (0.015) or It = B0 (0.99)t x (0.015) |
Minimum payment,
$,
Mt = Bt (0.025) or Mt = B0 (0.99)t x (0.025) |
| t = 0, Jan | B0 = 2000 | I1 = 30 | M1 = 50 |
| t= 1 | 1980 | 29.7 | 49.5 |
| 2 | 1960.2 | 29.4 | 49.01 |
| 3 | 1940.59 | 29.11 | 48.51 |
| 4 | 1921.19 | 29.82 | 48.03 |
| 5 | 1901.98 | 28.53 | 47.55 |
| 6 | 1852.46 | 28.24 | 47.07 |
| 7 | 1864.13 | 27.96 | 46.6 |
| 8 | 1845.49 | 27.68 | 46.14 |
| 9 | 1827.03 | 27.41 | 45.68 |
| 10 | 1808.76 | 27.13 | 45.22 |
| 11 | 1790.67 | 26.86 | 44.77 |
| t= 12 | B12 = 1772.76 | Sum = $340.84 |
So Bt = B0 (0.99)t = 2000 (0.99)t (From Series: B1= B0 + B0 (0.015) + B0( 0.025) )
It = B0 (0.99)t x (0.015) = 2000 (0.99)t ( 0.015)
Mt = B0 (0.99)t x (0.025)
(b) After one year unpaid balance is $1772.76.
You have paid $2000 - 1772.76 = $227.24
And total interest is the sum of interest column = $ 340.84
| Balance for 48 mts Bt
= B0 (0.99)t = 2000 (0.99)t
|
Interest and Payment Over 12 months
|