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 Martin’s account and let C represent the amount of money in Cary’s account.

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

Answer:

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

c = m = 200(1.05)^y

m = 1.22c

Step-by-step explanation:

The future value can be represented as :

Future value, F = P(1 + r)^n

r = interest rate = 5% = 0.05 , n = number of years ;

For Martin :

m = 200(1 + 0.05)^n

For cyan :

c = 200(1 + 0.05)^n

y years after Martin

Cyan opened 4 years after Martin :

Representing in terms of y

Cyan = y ; Martin = y +4

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

c = m = 200(1.05)^y

From. Indices :

(1.05)^y+4 = 1.05^y * 1.05^4

Hence,

m = 200 * 1.05^y * 1.05^4

c = 200 * 1.05)^y

Hence,

m = c * 1.05^4

m = c * 1.2155

m = c * 1.22

m = 1.22c