Problem 1. Peggy gets paid every other week (bi-weekly) and her husband Patrick gets paid monthly. Peggy is going to make a $150 deposit from her paycheck every two weeks into a new retirement fund, and Patrick is going to deposit $300 from his paycheck monthly into a new retirement fund. Both accounts earn an effective annual rate of 6%. Peggy's account compounds bi-weekly and Patrick's fund compounds monthly that matches their deposits.
a. What together can Peggy and Patrick expect to receive from their deposits in 30 years?
b. How much would Patrick have to deposit each month for the combined savings to achieve $1 million in thirty years? (Peggy would continue as above.)
Problem 2. Kim is evaluating her retirement plan. Suppose she has $500,000 when she retires in an account that earns at an effective annual rate of 9%.
a. If Kim withdraws $75,000 annually, how long will her funds last?
b. To make the funds last 25 years, how much can Kim withdraw annually?
c. Kim is considering a two phase withdrawal where she withdraws $60,000 annually for 10 years, and then $35,000 thereafter (when social security starts). How long will her funds last assuming that the 9% rate of return (EAR) is accurate for both phases of the retirement plan.
Problem 3. Peggy gets paid every other week (bi-weekly) and her husband Patrick gets paid monthly. Peggy is going to make a $150 deposit from her paycheck every two weeks into a new retirement fund, and Patrick is going to deposit $300 from his paycheck monthly into a new retirement fund. Both accounts earn an effective annual rate of 6%. Peggy's account compounds bi-weekly and Patrick's fund compounds monthly that matches their deposits.
a. What together can Peggy and Patrick expect to receive from their deposits in 30 years?
b. How much would Patrick have to deposit each month for the combined savings to achieve $1 million in thirty years? (Peggy would continue as above.)
Problem 4. John is going to buy a new car costing $24,000. Wealthy Uncle Job offered a choice of three loans as described below. The annual percentage rate with monthly compounding for all three alternative loans would be 3.25% and the loans would be for 4 years. Determine the payment amount that John would have to make for each loan alternative?
Loan 1 Loan 1 would be for the total cost of the car and John would pay equal monthly payments to Uncle Job .
Loan 2 Loan 2 would be for the total cost of the car with John making a $3,000 payment at the end of the loan and equal annual payments to Uncle Job for the remainder.
Loan 3 Loan 3 would have John using $3000 of his personal savings upfront to reduce the loan size and John would make equal monthly payments to Uncle Job.
Problem 5. Pat Davis has earned a promotion that will pay an annual bonus of $10,000 at the end of the first year and increase by 12% each year thereafter. He is going to deposit his annual bonus into a fund that has an annual percentage rate of 5% compounded monthly that presently has $30,000 in it. He plans to retire in 15 years. How much will be in the fund at the time he retires?