Edward deposits $250 each month into a retirement

account that pays 6.00% APR (0.50% per month). What is the value of this annuity after 20 years?

Edward deposits $250 each month into a retirement

account that pays 6.00% APR (0.50% per month). What is the value of this annuity after 20 years?

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Since you are looking for the future value (in 20 years) of this annuity, there is a simple mathematical formula you can use to make this calculation. The formula is as follows:

** FV = PMT * [ ((1 + i)**^{n}** - 1) / i ]** , where

**FV** = future value

**PMT** = amount of periodic payment = $**250** (per month)

**i** = interest rate (per month) = 0.50% / 100% = **0.005**

**n** = # of compounding periods = 20 years * 12 months/year = **
240** (payments for 20 years)

Plug in all these given values into the above formula:

**FV = 250 * [ ((1 + 0.005)**^{240}** - 1) / 0.005 ]**

**= 250 * [ (1.005**^{240}** - 1) / 0.005 ]**

** = 115,510.22379037**

** ≈ 115,510.22**

Thus, the value of this annuity after 20 years is approximately **
$115,510.22**

Academic honesty. I looked this formula up from text. It is too easy to make an error deriving it and I felt lazy.

P = A((1 + (i/q))^(n/q) - 1)(q/i)

where P is the principal after years

A is the amount deposited each interval (month)

i = interest rate (.06)

q = no. of pay periods/ year (12)

n = no of years. 20

= 115,510.22. Almost double the amount paid in (60000)

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