Question

Starting at age 35, you deposit $2000 a year into an ira account for retirement. Treat the yearly deposits into the account as a continuous income stream. If money in the account earns 7%, compounded continuously, how much will be in the account 30 years later, when you retire at age 65? How much of the final amount is interest?

Answer 1

Answer:

76.33 % is interest in Final Amount

Step-by-step explanation:

Interest for 1 st Year Deposit Amount for 35 Years

= P ( 1 + 7/100)³⁵ - P

similarly for 2nd Year Deposit Amount Inetrest for 34 Years

= P(1 + 7/100)³⁴ - P

till Last year deposit

Total interest = P (1.07³⁵ + 1.07³⁴ +.............................+ 1.07) - 35P

= P (1.07 + 1.07² +...................................+  1.07³⁴ + 1.07³⁵) - 35P

a Gp where a= 1.07 , r = 1.07  n = 35

= P  * 1.07  ( 1.07³⁵ - 1)/(1.07 - 1)   - 35P

= 147.913 P - 35P

= 112.913P

P = 2000

= 225826

Interest = 225826  $

Final Amount = 225826 + 35*2000 = 295826 $

Interest is  = (225826/295826) * 100 =  76.33 %