P 4-35 (similar to) li Question Help * You are saving for retirement. To live co

Question

P 4-35 (similar to) li Question Help * You are saving for retirement. To live comfortably, you decide you will need to save $1 million by the time you are 65. Today is your 28th birthday, and you decide, starting today and continuing on every birthday up to and including your 65th birthday, that you will put the same amount into a savings account. If the interest rate is 7%, how much must you set aside each year to make sure that you will have $1 million in the account on your 65th birthday? The amount to deposit each year is $ (Round to the nearest dollar.)

Explanation / Answer

Yearly amount needed to deposit in the account is $6237

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Your savings will be in the form of an annuity. Future value of the annuity is $1000000. Number of deposits made is 37, and the investment will earn interest rate of 7%.

FV of annuity = P [(1 + r)^n - 1]/ r

Let’s put all the values in the formula

1000000 = P[(1+0.07)37 – 1/0.07]

1000000 = P[(1.07)37 – 1/0.07]

1000000 = P[12.2236 – 1/0.07]

1000000 = P[11.2236/0.07]

1000000 = P * 160.3371

P = 1000000/160.3371

P = 6236.86 or $6237

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Hope this answer your query.

Feel free to comment if you have further query. J

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