. Louisa has $4,500 in her savings
account. She has to choose between two
savings plans. Under plan A, she will
increase her account balance by 10% per
year. Under plan B, her account balance
will increase by $525 per year.
If she plans to keep her money in savings
for 3 years, which plan should she
choose? How much more will she save
under that plan?
after n years, we have
A: 4500*1.10^n
B: 4500+525n
so, plug in n=3 and see which is greater, and by how much.
6500
To determine which plan Louisa should choose and how much more she will save, we need to compare the savings after 3 years for both plans.
For plan A, her account balance will increase by 10% per year. After the first year, she will have:
$4,500 + ($4,500 * 0.10) = $4,950
After the second year:
$4,950 + ($4,950 * 0.10) = $5,445
After the third year:
$5,445 + ($5,445 * 0.10) = $5,989.50
Under plan A, Louisa will have $5,989.50 after 3 years.
For plan B, her account balance will increase by $525 per year. After 3 years, her account balance will be:
$4,500 + ($525 * 3) = $4,500 + $1,575 = $6,075
Under plan B, Louisa will have $6,075 after 3 years.
Comparing the two plans, plan B will result in a higher savings balance after 3 years. She will save:
$6,075 - $5,989.50 = $85.50
Louisa should choose plan B because she will save $85.50 more compared to plan A.