Question

A friend creates an IRA (Individual retirement account) with an APR of 6.25%. She starts the IRA at the age of 25 and deposits $50 at the end of each month. How much will her IRA contain when she retires at the age of 65? a. $106,435.62 c. $106,601.32 b. $106,595.63 d. $106,613.15

Answer 1

b

Explanation:

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Answer 2

She will get $106,595.63 at the age of retirement.

Solution-

We know that,

`\text{FV of annuity}=P[((1+r)^n-1)/(r)]`

Where,

P = periodic payment

r = rate per period

n = number of period

Here,

`P=50,\\\\r = 6.25\%\ annually=(6.25)/(12)\%\ monthly=(6.25)/(1200)\ monthly\\\\n=40\ years=40* 12=480\ months`

Putting the values,

`\Rightarrow \text{FV of annuity}=50[\frac{(1.0052)^(480)-1}{{0.0052}}]`

`\Rightarrow \text{FV of annuity}=50[\frac{12.0556-1}{{0.0052}}]`

`\Rightarrow \text{FV of annuity}=106595.6257`

Therefore, she will get $106,595.63 at the age of retirement.