Question

# A new employee wants to make quarterly deposits in her investment plan. When she retires 30...

A new employee wants to make quarterly deposits in her investment plan. When she retires 30 years from now, she wants to have \$1,000,000 dollars deposited. Given the retirement plan pays 3% interest, what payment must she make?

Please show details and related formulas, I will give thumbs up ASAP.

Solution :

We have to use the below formula for an annuity, to calculate the deposits made.

Future value of an annuity = Deposits * [ {(1+r) ^ n - 1} / r ];

Here in this case n = 120; since the number of quarterly time periods in 30 years is (30* 4 = 120)

r = 3% and quarterly interest = 3% / 4 = 0.0075

Future value = \$ 1,000,000

Therefore plugging in the above values

1,000,000 = Deposits * [ {(1+0.0075) ^ 120 - 1} / 0.0075}

= Deposits * [ (2.451357 - 1) / 0.0075 ]

= Deposits * [ 1.451357 / 0.0075 ]

= Deposits * [ 193.514]

Re arranging the above equation,

Deposits = 1,000,000 / 193.514 = \$ 5167.577

Answer : New employee has to make quarterly deposits of \$ 5167.57 to have \$ 1,000,000 deposited at 30 years later.

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