Question

D vi 11/16/17 (1) An investor deposits $35,000 into an IRA for her retirement in 25 years. The account pays 3.5% interest compounded continuously. She also plans to deposit $1800 each year into the account in a near-continuous manner for the same amount of time. What will be the value of her account after 25 years if she stays true to this plan?

Answer 1

Soln orignal deposite (1) -$35,000 time period (it) = 25 years. interest rate (2= 3.5% or (i) = 0.035 Comp. annuall first calculate the amount , four, - P = $3.5000 we know that for calculating the amount over 'P' we need. to use the following formula. nt Where rate interest compounde i ne - te pa interest number of annually time, a Principle

. A. (1+ 0.035) Xsx (35,000) A.2 (1.035 ) x (35,000) A = 2.36324 X 35,000 TA $ 82, 713.5 so the amount for p $35.000 over 25 years is $ 82,7 13.5 Now as we know , investor deposited $ 1,800 each year, So now we need to calculate the amount for $1,800 each year. for this we will iyge the following formula where i interest De Deposited money

12 D 0.035 $1,800 1 + 1425 Ana 0.035 - 1 x(1800) 0.035 (1.035) 1 (1800) 2.36324-I X (1800) 1.36324 x1800) 0.035 2 38.94985 X 1800 An = $ 70,109.7 or $ 70 110 Hence the total value after 25 is - 23 8271 3.5 t 70109.7 2) $ 152,823.2 year

Thank you.