8. You are planning to retire 10 years from today (i.e. 10 years from today is a

Question

8. You are planning to retire 10 years from today (i.e. 10 years from today is at the end of year 10). Currently, you have $100,000 in a savings account growing at 5% per year (compounded annually and $300,000 in the stock market growing at 1 0% per year (compounded annually). You also plan on depositing $10,000 annually into your savings account for the next 10 years (assume end of year deposits with the first deposit at the end of year 1 and the last deposit at the end of year 10). If the interest rate on your savings account stays at 5% (compounded annually) and your stocks continue to grow at 10% (compounded annually, how much will you have in total at the end of 10 years?

Explanation / Answer

Current balance in savings account = $100,000

Interest rate in savings account = 5% per year

Compund value factor at 5% for 10 years (CVF5% , 10 ) = 1.629

Hence, current balance in savings account will grow to after 10 years = 100,000 x 1.629

= $162,900

Current balance in stock market = $300,000

Growth rate in stock market = 10% per year

Compund value factor at 10% for 10 years (CVF10% , 10 ) = 2.594

Hence, current balance in stock market will grow to after 10 years = 300,000 x 2.594

= $778,200

$10,000 are deposited annually in the savings account for the next 10 years growing at 5% annually.

Compound value annuity factor at 5% for 10 years (CVAF5%, 10) = 12.578

Hence, $10,000 deposited annually in the savings account at 5% will grow to after 10 years = 10,000 x 12.578

= $125,780

Hence, total amount available after 10 years will be = 162,900 + 778,200 + 125,780

= $1,066,880

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