Question

Today is your 25th birthday, and you want to save $1.1 Million by your birthday at age 70. If you expect to earn 8% APR compounded monthly in your retirement account, what constant payment at the end of each month must you deposit into the account through your 70th birthday in order to reach your retirement savings goal on your 70th birthday? (Answer to the nearest penny.)

Answer 1

The amount is computed as shown below:

Future value = Monthly deposits x [ [ (1 + r)ⁿ – 1 ] / r ]

r is computed as follows:

= 8% / 12 (Since the interest is compounded monthly, hence divided by 12)

= 0.666666667%

n is computed as follows:

= (70 - 25) x 12

= 540

So, the amount will be as follows:

$ 1,100,000 = Monthly deposits  x [ [ (1 + 0.006666667)⁵⁴⁰ - 1 ] / 0.006666667]

Monthly deposits = $ 1,100,000 / x 5,274.540598

= $ 208.55 Approximately

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