Question

please answer all of the following questions

21. Suppose you deposit $5,000 into an account earning 4 percent interest, compounded monthly and you also make monthly contributions of $50 (first monthly contribution made one month after the initial deposit is made). How many years (rounded to one decimal place --for example, 32.1843 year = 32.2) will it take for the account to grow to $7,500 in this case? 22. Assume that I am trying to borrow money from you to finance my business. Assume that I promise to repay you in three installments, one payment of $5,000 to be made exactly 2 years from today, a second payment of $10,000 to be made exactly 5 years from today, and a final payment of $15,000 to be made 8 years from today. If your opportunity cost of funds is 7.5% p.a., (that is, use an interest rate of 7.5% for this question), how much should be willing to lend me today? 23. What is the future value at the end of year 28 of depositing $5,000 today, $3,500 at the end of years 1. 2 and 3, S5,000 at the end of years 4, 5, 6 and 7 and $4,250 at the end of years 8, 9, 10, 11 and 12 into an account that pays 9.5% p.a.? (No deposits will be made into the account after year 12). 24. If you wanted to fund a scholarship that would pay $12,500 per year forever at GSU, how much would you have to deposit today if you wanted the scholarship to start paying six (6) years from today? Assume the endowment could earn 6.25% p.a. interest forever,

Answer 1

As per HOMEWORKLIB RULES, 4 questions need to be posted as separate questions. We can only answer first question by default in the absence of any specifics.

Answer for first question,

No. of payments made in a year = 12 (monthly payments)

Present value of money = -5000

Interest rate = 4/12 or 0.33 compounded monthly

Future value of money = $7500

Payment made each month = $50

Using a financial calculator to add all the above inputs, we get 2.95 years as the value of N or number of years required to grow the account to $7500.

Alternatively, you can also use the below formula to calculate the answer by hand :

FV = PV x [ 1 + (i / 12) ] ^{(12 x no. of years)} for each payment made.