Question 1132927
5941+6636 = 12577
P(1+(0.045/12))^12*15 = 12577
P(1.00375)^180 = 12577
P*1.9616 = 12577
P = 6411.60 
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NOTE: In your calculations you used 5 years but in the problem you posted you say 15 years, so I used 15 years. By the way, there's nothing wrong with your calculations.
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Here it is with 5 years:
P(1+(0.045/12))^12*5
P(1.00375)^60
P*1.2518 = 12,557
P = 10,031.16 (same answer you got, this is how much they initially saved)