In March, a family starts saving for a vacation they are planning for the end of August. The family expects the vacation to cost $1483. They start with $120. At the beginning of each month they plan to deposit 25% more than the previous month. Will they have enough money for their trip? If not, how much more do they need?
Accepted Solution
A:
No, They will need 131.94 more dollars. The exponential growth formula can help us find how much is to be deposited each month and then adding them together for the 5 months after the initial deposit will give us the amount saved. [tex]y=a(1+r)^{x} [/tex] a is the initial value (120) r is the rate of growth (0.25) x is time [0,1,2,3,4,5) March [tex]120(1+.25)^{0} = 120[/tex] April [tex]120(1+.25)^{1} = 150[/tex] May [tex]120(1+.25)^{2} = 187.5[/tex] June [tex]120(1+.25)^{3} = 234.38[/tex] July [tex]120(1+.25)^{4} = 292.97 [/tex] August [tex]120(1+.25)^{5} = 366.21[/tex]
Totals 120+150+187.5+234.38+292.97+366.21= 1351.06 totalt saved by august