Problem Set 3 - Compound Interest

a)You deposit 2000 TL in a bank account paying 8% interest per year. Determine how much interest your investment will earn in 5 years in this account if (i) the interest is simple and (i) if the interest is compound.

b)You borrow 20,000 TL at 10% yearly interest (compounded annually). You will not make any payment in the first year. In Years 2, 3 and 4 you will make equal end-of-year payments of A TL to pay off the loan at the end of Year 4. You can assume that all of a years interest is paid off at the end of that year (except, of course, on Year 1 when there is no payment). Based on this information, frst calculate the value of A that will make this payment arrangement valid and complete the table below that will show the year-by-year status of the loan balance.

Year	Beginning of Year Balance	Interest Accrued for the Year	Total Balance	Payment Towards Years Interest	Payment Towards Remaining Balance	Total Payment	End of Year Balance
1
2
3
4
Total

c)You deposit 3,000 TL today in a bank account that pays 0.75% monthly interest. How many months will it take for the money to grow to double? Calculate your answer analytically and by using a relevant Excel function.

d)Your late grandfather bought a farmland 30 years ago for 1,000 TL, which he recently sold for 160,000 TL. What yearly interest did he earn on this investment? Calculate your answer analytically and by using a relevant Excel function.

e)You want to save 1,000,000 TL by making uniform monthly deposits in a bank account paying 0.8% interest per month. If you want to achieve you goal in 20 years, how much should you deposit each month? Calculate your answer analytically and by using a relevant Excel function.

f)Your father just retired with 555,000 TL savings in his private retirement account that pays 0.92% monthly interest. If he wants to withdraw a salary of 6,000TL per month, how long will it take for him to deplete the savings? As a graduate student with excellent knowledge engineering economics, you advice him to be more conservative and withdraw 5,100 TL per month (15% less than his original intention of 6,000 TL). How long will the retirement savings last then? Show your calculations both using analytical formulas and a relevant Excel function. Interpret your findings.

g) In reference to part (f) above, your farther agrees with you that he can be more conservative with cashing into his retirement savings. As a person with years of Engineering Economics experience in his career, he is well capable of making his own calculations. He immediately understands that your real motivation could as well be maximizing your inheritance of the amount of money left in the account upon his death (at which he takes no offense). But he explains that the real reason he wants to withdraw 6000 TL a month is because he wants to put part of that money into a different retirement account that he can lock in a monthly rate of 1% (if he commits to making no withdrawals for the first 15 years). The current account allows him to withdraw at most 6000 TL a month, and he claims that at that withdrawal rate his calculations show that he will deplete the money in roughly 208 months. For all these months, his plan is to put 810 TL into the new retirement account (thus leaving him with 5190 TL to spend), which he claims will grow to be a larger amount of money than would be in the current account if he implemented your suggestion of withdrawing only 5100 a month. Verify your fathers calculations.