Question

There are five finance questions. Please explain more detail and list your formula. Thanks

1. Sue started a retirement savings plan. At the end of each year, for 25 years, Sue deposited $4,000 to her savings plan. If the retirement savings plan earns 4 percent, compounded annually, what will her account balance equal after Sue makes the last of her 25 annual savings deposits?

2. Tom was injured by a vehicle driven by a Rapid Transit delivery driver. To settle the claim for Tom's injuries, Rapid Transit agreed to pay Tom ten annual payments of $20,000 with the first of these payments three years from today. Assuming a 4 percent annual interest rate, what is the present value of Tom's settlement?

3. To settle a wrongful death case, a judge ordered the maker of a defective product to pay the spouse of the deceased person $90,000 today, $150,000 three years from today, and $500,000 six years from today. What is the present value of the judgement against the product manufacturer, assuming a 5 percent annual interest rate? (note--the payment "today" is part of the judgement)

4. Allen would like to purchase a new home. To help fund the purchase, she will borrow $180,000 from her credit union. Jenna agreed to make monthly payments for 15 years (180 months) to repay the loan. The credit union will charge 9 percent interest, compounded monthly (0.75 percent per month). What is Jenna's monthly mortgage loan payment?

5. Jade Company borrowed money by issuing some 12-year bonds. When the bonds mature after twelve years, Harris will have to pay the maturity value, $15 million, to the bondholders. Harris Company would like to pre-fund the $15 million by setting aside an equal annual amount at the end of each year for 12 years. If the funds set aside to pre-fund the $15 million can earn 5 percent annual interest, how much must Harris Company set aside in an equal amount at the end of each year so that after 12 years it will have the money needed to pay-off the bondholders?

Answer 1

Part 1)
Interest rate = r, Deposit amount=p, number of year=n
Account balance after 25 years = P + {P*(1+r)*[(1+r)^(n-1) -1]/r} = 4000+{4000*(1+0.04)*[(1+0.04)^(25-1) -1]/0.04} = 4000+{100000*1.04*[(1.04^24)-1]} = 4000+{104000*(2.563304165-1)} = 4000+{104000*1.563304165} = 4000+162583.63 = $166,583.63

Part 2)
Value of Tom's settlement 3years from today = annual payment*{1-[(1+r)^(-n)]}/r = 20000*{1-[(1+0.04)^(-10)]}/0.04 = 500000*{1-[1.04^(-10)]} = 500000*{1-0.6755641688} = 500000*0.3244358312 = $162,217.92
Present value of Tom's settlement = Value of Tom's settlement 3years from today/[(1+r)^3year] = $162,217.92/[(1+0.04)^3] = $162,217.92/(1.04^3) = $162,217.92/1.124864 = $144,211.14

Part 3)
Present value of judgement = $90000 + $150000/[(1+0.05)^3] + $500000/[(1+0.05)^6] = $90,000 + $150,000/(1.05^3) + $500,000/(1.05^6) = $90,000 + $150,000/1.157625 + $500,000/1.340095640625 = $90,000+$129,575.64+$373,107.70 = $592,683.34

Part 4)
Loan amount(p) = $180,000, r=9%/12 = 0.75%, n=180months
Monthly mortgage payment = p*r*[(1+r)^n]/[(1+r)^n -1] = $180,000*0.0075*[(1+0.0075)^180]/[(1+0.0075)^180 -1] = 1350*[1.0075^180]/[(1.0075^180)-1] = 1350*3.838043267/2.838043267 = $1,825.68

Part 5)
Annual payment = Future value*r/[(1+r)^n -1] = 15,000,000*0.05/[(1+0.05)^12 -1] = 750,000/[(1.05^12)-1] = 750,000/(1.795856326-1) = 750,000/0.795856326 = $942,381.15