SOLUTION: Mary saves $20 the first week. She saves an additional 10% each week. How much will she save on the seventh week?

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Mary saves $20 the first week. She saves an additional 10% each week. How much will she save on the seventh week?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 544013: Mary saves $20 the first week. She saves an additional 10% each week. How much will she save on the seventh week?
Answer by jpg7n16(66) About Me  (Show Source):
You can put this solution on YOUR website!
Well since we're trying to find how much she saves each week, let's look to see what pattern forms:
Week1+=+20
Week2+=+20%2A1.10+=+22
Week3+=+22%2A1.10+=+%2820%2A1.10%29%2A1.10+=+20%2A%281.10%5E2%29+=+24.20
Week4+=+24.20%2A1.10+=+%2820%2A1.10%2A1.10%29%2A1.10+=+20%2A%281.10%5E3%29+=+26.62
Have you spotted the pattern yet? It's always 20%2A%281.10%5Ex%29 where the exponent is always the # of the week, minus 1. (Week2 was 20%2A%281.10%5E1%29)
.
So use the following formula:
A=p%2A%281.10%29%5E%28n-1%29
"A" = amount saved
"p" = initial amount
"n" = number of weeks
.
So for instance, week 1:
A=p%2A%281.10%29%5E%28n-1%29
A=20%2A%281.10%29%5E%281-1%29
A=20%2A%281.10%29%5E%280%29=20%2A1=20
.
Or week 4:
A=p%2A%281.10%29%5E%28n-1%29
A=20%2A%281.10%29%5E%284-1%29
A=20%2A%281.10%29%5E%283%29=20%2A1.331=26.62
.
Both of which we know to be true from our examples above. But now you know how to calculate week 7, 17, or 700 (if needed). Hope this helps!