Question 1

The cost of a new automobile is $30,000. If the interest rate is 8%, how much would you have to set aside now to provide this sum in ten years? Assume interests are compounded annually and the cost of the car does not appreciate over those ten years.

a) How much will you have at the end of 25 years if you invest $300 today at 11% annually compounded?

b) How much will you have if you invested at 11% continuously compounded?

Question 2

The Murphy family are planning to buy a new home. The house costs $1,000,000, but the family have $415,000 in savings that they can use as down-payment. The remainder is to be financed by a mortgage. Their bank offers a 25-year loan, with fixed interest at 9.6% (per annum), with fixed monthly payments.

a) What are the monthly payments that the Murphys will have to make so that the entire mortgage is paid off in 25 years?

b) If the Murphys can afford to pay $5,000 per month, can they afford the house? If not, how much additional down-payment would they require?

c) Now suppose the family pays $6,500 per month instead. Can they pay off their mortgage in 15 years without increasing their down-payment?

Question 3

The Murphy family, whose acquaintance we have made earlier, are setting up a retirement plan. They will make fixed monthly contributions to a pension fund, until Mr and Mrs Murphy retire, that is, 35 years from now. After retirement, the family are planning to withdraw a fixed amount C each month for the next 25 years. Assume a fixed 7.8% annual discount rate.

a) If the Murphys plan to withdraw $3,000 each month, how much would they have to pay into the fund each month before they retire?

b) How much can the family withdraw each month after retirement, if they can only afford to contribute $200 each month to the fund now?