# If you wanted to have \$1,000,000 in savings at retirement, how much would you need to save each year over the next 30 years if you could earn 5% annually on your savings?

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You need to save \$1,000,000 in the next 30 years; your investment earns 5% annual interest.

Your present value PV is zero, the future value FV is \$1,000,000, the interest rate i is .05, and the number of periods is 30. (Assuming that you are making yearly payments.) We are looking for the annual payment C:

The formula is FV= C * ((1+i)^n-1)/i)

(This comes from the sum of a finite number of terms of a geometric series.)

1000000=C*((1.05)^30)/.05)

1000000=C * 66.4388

C=15051.44

You would need to save \$15051.44 each year at 5% to have 1000000 after 30 years.

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Note that if you made monthly installments (instead of lump sum yearly installments), still earning 5% annual interest (assuming the interest is paid monthly) you would only have to save \$14,418.60. This comes from the fact that your installments accrue interest -- we use the same formula but now n=360 (the number of compounding periods is 30*12=360.) The monthly payments are \$1201.55

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