You are saving for retirement. To live comfortably, you decide you will need to

Question

5. You are saving for retirement. To live comfortably, you decide you will need to save $2 million by the time you are 65. Today is your 30th 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 5%, how much must you set aside each year to make sure that you will have $2 million in the account on your 65th birthday? Solve for the end of period.

5. You are saving for retirement. To live comfortably, you decide you will need to save $2 million by the time you are 65. Today is your 30th 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 5%, how much must you set aside each year to make sure that you will have $2 million in the account on your 65th birthday? Solve for the end of period.

Explanation / Answer

Number of deposits = 36

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

Let's put the values in the formula,

2000000 = P* [(1 + 0.05)^36 - 1]/ 0.05

2000000 = P* [(1.05 )^36 - 1]/ 0.05

2000000 = P* ( 5.791816136 ) - 1/ 0.05

2000000 = P* ( 4.791816136 )/ 0.05

2000000 = P* 95.83632272

P = 2000000/ 95.83632272

= 20868.91

So you need to deposit 20868.91 each year at the end of the year.

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