Financial Planning and Analysis: Investment Account, Present Value, Retirement Savings Plan

Calculating the Balance of an Investment Account

1. What is the balance in an investment account at the end of 10 years if $5,000 is invested today and the account earns 8% interest compounded annually? What would the value be after 50 years? After 100 years?
2. What is the present value of the following future amounts:
Future Value Discount rate Number of periods
$15,000 6% 5
$37,000 9% 10
$596,000 11% 4
$1,178,000 9.5% 12
3. Calculate the present value of the following cash inflows assuming an 11% discount rate.
Year Cash flow
1 17,000
2 17,000
3 17,000
4 17,000
5 17,000
6 100,000
4. Anne Jones checked her lottery ticket once again. The numbers matched; she had won the $10,000,000 grand prize. The lottery provided two options for payment of the grand prize. First, the winner could take $1,000,000 immediately, with the remainder payable in $1,000,000 instalments over nine years, starting one year from now. The alternative payment option was an immediate lump sum payment of $7,000,000. Anne believes that she can earn a rate of return of 7 per cent on any money she receives.
a) Which payment option would you suggest that Anne select?
b) What Interest rate would make these two options equivalent?
5. You are planning to establish a retirement savings plan by setting aside money at the end of each year. It is your hope to retire at age 55 with a pension income of $100,000 per year received at the end of each year, for 20 years, from the money accumulated in this fund. You expect to earn 8% per year on the fund assets as they accumulate, and on retirement, you expect to purchase a 20 year annuity earning 6% on the undrawn balance. You are now 30 years of age. Ignore inflation.
a. How much money will be required in the retirement fund to purchase the annuity when you are 55?