Question

Julia deposits $2000 into a savings account that

earns 4% interest per year. The exponential
function that models this savings account is
y = 2000(1.04), where t is the time in years.
Which equation correctly represents the amount
of money in her savings account in terms of the
monthly growth rate?

Please show work

Answer 1

C.

Explanation:

Yearly compounding.
y = 2000(1.04)^t

Monthly compounding.

y = 2000(1 + r/12)^(12t)

2000(1.04)^t = 2000(1 + r/12)^(12t)

(1.04)^t = (1 + r/12)^(12t)

(1.04^t)^(1/t) = [(1 + r/12)^(12t)]^(1/t)

1.04 = (1 + r/12)^12

1.04^(1/12) = [(1 + r/12)^12]^(1/12)

1.00327374 = 1 + r/12

y = 2000(1.00327374)^(12t)

Answer: C.