Martin deposits $200 in a savings account that earns 5% annual interest. four years later, cary deposits $200 in an account earning the same interest. let m represent the balance in martins account and let c represent the amount of money in carys account. choose the pair of expressions that describe the accounts y years after martin opened his account. martin: 200(1.05)y cary: 200(1.05)y+4 martin: 200(1.05)y+4 cary: 200(1.05)y4 martin: 200(0.05)y cary: 200(0.05)y4 martin: 200(1.05)y cary: 200(1.05)y4 choose the equation that relates the balances in the accounts y years after martin opened his account. c = m(1.05)4y m = c(1.05)4y c = 1.22m m = 1.22c

The formula for the amount of money in an account gaining interest is:

F = P * (1 + i)^n

Where,

F = future value of the money / money with interest

P = present value of money / money invested

i = interest rate

n = number of years

Assuming that y = number of years that Cary has deposited and since Martin has started 4 years ahead therefore n for Martin is y + 4. By establishing that, we get these equations:

Martin, m = 200 * (1.05)^(y + 4)

Cary, c = 200 * (1.05)^y

Since Martin’s equation can also be written as:

m = 200 * (1.05)^y * (1.05)^4

Therefore we can relate the equations for Martin and Cary:

m = c * (1.05)^4

m = 1.22 c

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