Question

You are planning to start investing so that you can retire in 22 years. If you would like to have $2305392 when you retire and if you think you can earn 10.38% per year on average, how much will you have to deposit each waek to meet your goal? Enter only numbers and decimals in your

response round o decimal places

Answer 1

$523.56

Explanation:

You want the amount to deposit weekly to have $2,305,392 at the end of 22 years, if the deposit earns an annual rate of 10.38%.

Annuity

If we assume the interest is compounded weekly, and there are 52 weeks in a year, then value of the account will be given by the annuity formula:

A = P(n/r)((1 +r/n)^(nt) -1)

where P is the payment amount, r is the annual rate, n is the number of times it is compounded per year, and t is the number of years.

Payment

Solving for P gives ...

P = A·r/(n·((1 +r/n)^(n·t) -1))

P = 2305392(0.1038)/(52·((1 +0.1038/52)^(52·22) -1)) ≈ 523.56

You need to deposit $523.56 each week to meet your retirement goal.

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Additional comment

There is 1 additional day each year, except leap years have 2 additional days. This means in 22 years, there will be more than 3 additional weeks. These extra payments will potentially affect the result.

If compounding is at some interval other than weekly, the result will be different. If compounding is monthly, a payment of $529.00 may be required.

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