Your bank account increases by 5% each month. Right now you have $200,000 how much money did you have 2 months ago?

Question

Topic: Sequences

the equation is:

t(n) = 200,000 • 1.05ⁿ

do we divide by 1/1.05 and make n = 2

Answer 1

I would use your given equation and just plug in 2 for n.

t(n) = 200,000 x 1.05^{n (original equation)}

t(2) = 200,000 x 1.05^{2 (plugging in 2 for n)}

t(2) = 200,000 x 1.1025 (simplifying)

t(2) = 220,500 (solving for t)

2 months ago, there was $220,500 in the account.

Answer 2

100% is all of it

100% + 5% = 105% = 1.05

x was the amount 2 months ago....

1.05X is the amount last month,

1.05^2 x is the amount this month

200000 = 1.05^2 * X

X = 200000/(1.05^2) = 181405.90