EXERCISES: TIME VALUE OF MONEY

QUESTION 1

Your friend is celebrating her 35^th birthday today and wants to start saving for her anticipated retirement at age 65. She wants to be able to withdraw RM120,000 from her savings account on each birthday for 20 years following her retirement; the first withdrawal will be on her 66^th birthday. Your friend intends to invest her money in a local bank which offers 7 percent interest per year. She wants to make equal annual payments on each birthday into this account for her retirement fund.

If she starts making these deposits on her 36^th birthday and continues to make deposits until she is 65 (the last deposit will be on her 65^th birthday), what amount must she deposit annually to be able to make the desired withdrawals at retirement?

Suppose your friend has just inherited a large sum of money. Rather than making equal annual payments, she has decided to make one lump-sum payment on her 35^th birthday to cover her retirement needs. What amount does she have to deposit?

Suppose your friends employer will contribute RM2,500 to the account every year as part of the companys profit-sharing plan. In addition, your friend expects a RM30,000 distribution from a family trust fund on her 55^th birthday, which she will also put into the retirement account. What amount must she deposit annually now to be able to make the desired withdrawals at retirement?

QUESTION 2

Eight years from today, Azim expects his son will be entering college. He intends to save for his sons college expenses. He estimates that the four-year college expenses would be RM15,000 for the first three years and RM20,000 for the final year with the first payment will be made as his son registered for enrollment. To realise his plans, Azim opens an account and deposits RM5,000 today. He makes an arrangement to deposit a certain fixed amount each year, starting one year from now for the next eight years. This means that immediately after his last deposit, the first withdrawal would take place as at that time, his son will start his college. If the account earns 10 percent, what is the amount that Azim has to deposit each year into the account so that his son will have enough money to withdraw each year while he is in college?