## Answers

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

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