Assume that you have a balance of $4500 on your Discover credit card and that you make no more charges. Assume that Discover charges 27% APR and that each month you make only the minimum payment of 2% of the balance. What will the balance be after 32 months?
(Round your answer to the nearest cent.)
I took the "balance" to mean "principal + interest" at the end of each month. Because the interest of 27% APR =0.27/12 =2.25% per month, is greater than the minimum payment of 2%, the loan will continue to grow bigger and bigger each month for 32 months.
a=4500;p=1; b=(0.27/12 + 1);c=(a*b - 0.02*a*b);a=c;printp,"-",c; p++;if(p<=32, goto3, 0)
OUTPUT:
1 - 4509.23
2 - 4518.47
3 - 4527.73
4 - 4537.01
5 - 4546.31
6 - 4555.63
7 - 4564.97
8 - 4574.33
9 - 4583.71
10 - 4593.11
11 - 4602.52
12 - 4611.96
13 - 4621.41
14 - 4630.89
15 - 4640.38
16 - 4649.89
17 - 4659.42
18 - 4668.98
19 - 4678.55
20 - 4688.14
21 - 4697.75
22 - 4707.38
23 - 4717.03
24 - 4726.7
25 - 4736.39
26 - 4746.1
27 - 4755.83
28 - 4765.58
29 - 4775.35
30 - 4785.14
31 - 4794.95
32 - 4804.78
+23246 You start with $4500.00.
Each month the credit card company adds onto this an amount of interest:
since it si 27% per year, it will be a multiple of 0.27/12 and added onto the previous balance
this can be found by multiplying the old balance by (1 + 0.27/12)
After this, each month your payment of 7% is deducted from the amount owed:
this can be found by multiplying what you owe by 0.93 (if you pay off 7%, you still owe 93%)
To do this for 32 months, you have to do this 32 times:
since it requires multiplying 32 times, you can just raise the multiple to the power of 32.
4500 x [ (1 + 0.27/12) x (0.93) ]32
I got an answer of slightly under $900.00
