1. Your bank charges an interest rate of 4% on all borrowings. If you can afford to pay $1,000 per year to repay a loan, how much will you bank lend you today for a 20 year loan?
2. Suppose you are planning to save for retirement, and you estimate that you can save/invest $2,000 at the end of each year while you are working. If you expect to earn an annual return of 8% on your savings/investments, how much money will you expect to have in your retirement account when you retire in 45 years?
3. You plan to retire in 40 years and you estimate that you will need $2 million in your retirement account on the day you retire to fund your retirement living expenses.
a. If you expect to earn an annual return of 8% on your investments, what constant amount do you need to invest at the end of each year to meet your goal if you start investing this year?
b. If you expect to earn an annual return of 8% on your investments, what constant amount do you need to invest at the end of each year to meet your goal if you wait eleven years to start investing?
4. On the day you retire you expect to have $2 million in your retirement account to fund your retirement living expenses. After retiring, you expect to live an additional 25 years.
a. If you expect to earn a return of 8% on any funds in your retirement account, what is the largest constant amount you can withdraw from your retirement account each year while retired?
b. Upon your death, you would like to leave an inheritance of $0.5 million to your child. Considering this, if you expect to earn a return of 8% on any funds in your retirement account, what is the largest constant amount you can withdraw from your retirement account per year while retired?
5. You expect that you will live for 30 years in retirement. If you expect to earn a return of 8% on any funds in your retirement account and will need $60K per year to fund your retirement living expenses, how much money do you need to have in your retirement account on the day you retire?
6. Suppose I offer to give you $10/year forever if you pay me $150 now. Is this a good deal for you if the interest rate is 6%?