You need to have $1,000 in two years. You want to save an equal amount next year

Question

You need to have $1,000 in two years.  You want to save an equal amount next year and the following year (at years one and two) to have this $1,000.  The interest rate for the first year is 4% and the rate for the second year is 6.5%. What is the amount you need to save?

Assume you have $10,000 in the bank now and you will deposit and additional $5,000 a year for the next 20 years (as a regular annuity).  You will then withdraw the money as a regular annuity over the next ten years.  If the interest rate is 10% for the entire period what are the amounts of the annuity withdrawals?

Explanation / Answer

The answer to the first question is $475.06. If you earn 4% the first year, you earn $494.06 in year 1. If you earn 6.5% in the second year, you earn $505.94 in year 2. Total is $1000 with the initial deposit and the interest earned by the end of year 2.

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