Question

You are planning to make annual deposits of $6,090 into a retirement account that pays 9 percent interest compounded monthly. How large will your account balance be in 30 years? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.)

Answer 1

Given,

Annual deposits (A) = $6090

Interest rate = 9% or 0.09

Number of years (n) = 30 years

Solution :-

Effective annual rate (r) = [1 + (interest rate/12)]¹² - 1

= [1 + (0.09/12)]¹² - 1

= [1 + 0.0075]¹² - 1

= [1.0075]¹² - 1

= 1.0938068976 - 1 = 0.0938068976

Now,

Future value = A/r x [(1 + r)ⁿ - 1]

= $6090/0.0938068976 x [(1 + 0.0938068976)³⁰ - 1]

= $6090/0.0938068976 x [(1.0938068976)³⁰ - 1]

= $6090/0.0938068976 x [14.730576094362 - 1]

= $6090/0.0938068976 x 13.730576094362 = $891397.23

Your account balance will be $891397.23 in 30 years.