Question

suppose that one opens an individual retirement account (IRA) at age 25 and makes annual investments of $2000 thereafter in a continuous manner. Assuming a rate of return of 8%, what will be the balance in the IRA at age 65?

Answer 1

Answer: Value of IRA when one turns 65:

Future value (compounded continuously) = yearly installment amount × [( e^rt - 1)/(e^r - 1)]

e = 2.718281828

Yearly installment amount : P = $2,000

Rate of interest : r = 8% = 0.08

Number of payments made in 40 years : t = 40

(65 - 25 = 40 years)

= 2,000 × [(e^0.08×40 - 1)/(e^0.08 - 1)]

=2,000 × [(2.718281828^3.2 - 1) / (2.718281828^0.08 - 1)]

= 2,000 × [(24.53253 - 1) / (2.22554 - 1)]

= 2,000 × [(23.53253) / (1.22554)]

= $38,403.5282

or $38,404