Answer:
- A: 400·(1 +0.02)^48
- C: 400·(1.27)^4
- E: 400·((1.02)^12)^4
Explanation:
You want the equivalent expressions for the amount due on a credit card that compounds interest at 2% per month for 4 years on an initial balance of $400.
Compound interest
The amount resulting from a principal P earning compound interest at rate r per month for n months is ...
A = P(1 +r)^n
For P = 400, r = 2% and n = 48 months, this is ...
A = 400·(1 +0.02)^48 . . . . . matches choice A
We can divide this expression into a factor that represents the multiplier each year for 4 years:
A = 400·((1 +0.02)^12)^4
A = 400·((1.02)^12)^4 . . . . . matches choice E
Evaluating the inner parentheses, we get ...
A = 400·(1.27)^4 . . . . . matches choice C
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Additional comment
1.02^12 ≈ 1.26864 ≈ 1.27
By rounding up to 1.27, the final balance will be about $6 more than it would be if a more precise number were used. $1041 vs. $1035.
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