1. Andrew deposits $500 from each of his monthly paychecks into a 401(k) savings plan at work. He will keep this up for the next 37 years, at which time he plans to retire, hopefully having accumulated a large balance in his account.
a. Is the value of the account when he retires a present value or a future value?
b. Is this an ordinary annuity or an annuity due?
2. Jennifer borrowed $225,000 to buy a house. To pay off this mortgage loan, she agreed to make monthly payments at the beginning of each billing cycle.
a. Is the amount she borrowed a present value or future value?
b. Is this an ordinary annuity or an annuity due?
3. Find the future value annuity factor for a term of 29 years with an interest rate of 6.75% compounded annually.
4. Suppose that Ryan deposits $350 each month for 25 years into an account paying 5 3/8% interest. What will the future value of the account be?
5. How much total interest did Ryan earn in problem #4?
6. Tiffany plans to deposit $4,500 at the beginning of each year into a retirement savings account. Assuming that she continues these deposits, and that her account earns 7.5% compounded annually, how much money will she have accumulated after 36 years?
7. Patrick plans to start graduate school in 4 years after obtaining an undergraduate degree. He determines that he will need to save up $60,000 in 4 years. He decides that he will make weekly deposits into an investment account. How much money will he need to deposit each week, assuming that his savings earn 3.25% interest?
8. Assume that you are 24 years old and hope to be able to retire 43 years from now, at age 67. To ensure that you can do so comfortably, you decide to start making deposits into an investment account which you assume can earn an average of 6% interest. The deposits will be automatically deducted from your biweekly paycheck. To get some sense of how large your deposits should be, you set a goal of having $850,000 in your retirement account. Determine how much you should deduct from each paycheck to reach your goal.
9. Determine the total amount of interest you will be earning in problem #8.
10. Nick just graduated from college and is thinking about buying a car. He determines that he can afford monthly loan payments of $400, and that he would be taking out a 5-year loan with an interest rate of 4.9%. What is the most he can afford to pay for a car?
11. Sean and Jillian are buying a house and will need to take out a $200,000 mortgage loan. They plan to take out a standard 30-year mortgage loan with an interest rate of 3 7/8%. Find their monthly payment.
12. Find the total amount of interest Sean and Jillian will pay for their 30 year mortgage in problem #11.