Your generous grandmother has just announced that she’s opened a savings account for you with a deposit of $10,000. Moreover, she intends to make you 9 more similar gifts, at the end of this year, next year, etc. If the savings account pays 8% interest, how much will you have accumulated at the end of 10 years (one year after the last gift)? (Answer: $156454.87)
John is turning 13 today. His birthday resolution is to start saving towards the purchase of a car that he wants to buy on his 18th birthday. The car costs $15,000 today, and he expects the price to grow at 2% per year. John has heard that a local bank offers a savings account which pays an interest rate of 5% per year. He plans to make 6 contributions of $1,000 each to the savings account (the first contribution to be made today); he will use the funds in the account on his 18th birthday as a down payment for the car, financing the balance through the car dealer. He expects the dealer to offer the following terms for financing: 7 equal yearly payments (with the first payment due one year after he takes possession of the car); an annual interest rate of 7%. a. How much will John need to finance through the dealer? (Answer: $9759.30) b. What will be the amount of his yearly payment to the dealer? (Answer: $1810.87)
Mary has just completed her undergraduate degree from Northwestern University and is already planning on entering an MBA program four years from today. The tuition will be $20,000 per year for two years, paid at the beginning of each year. In addition, Mary would like to retire 15 years from today and receive a pension of $60,000 every year for 20 years and receive the first payment 15 years from today. Mary can borrow and lend as much as she likes at a rate of 7%, compounded annually. In order to fund her expenditures, Mary will save money at the end of years 1-3 and at the end of years 6-14. Calculate the constant annual dollar amount that Mary must save at the end of each of these years to cover all of her expenditures (tuition and retirement)? (Answer: $38254.77)
You’re 55 years old today, and you wish to start saving for your pension. Here are the parameters: • You intend to make a deposit today and at the beginning of each of the next 9 years (that is, on your 55th, 56th, …, 64th birthdays). • Starting from your 65th birthday until your 84th, you would like to withdraw $50,000 per year (no plans for after that). • The interest rate is 12%. How much should you deposit in each of the initial years in order to fully fund the withdrawals? (Answer: $21282.00)
Cooper corporation has borrowed $120,000 from the bank at 8% annual interest rate, compounded monthly. The company plans to pay $2000 per month for the first 12 months, and then pay $2500 per month for the next 12 months. Find the remaining balance of the loan after 24 months. (Answer: $82655.21)
Akron Corporation has borrowed $1.2 million from a bank with the understanding that they will pay $50000 a month until it pays off the loan. The bank will charge 9% annual interest, compounded monthly. Akron will make the payments at the end of each month. Find the following: a. How long will it take Akron to pay off the loan; (Answer: 26.56 months) b. What is the balance of the loan after 24 months? (Answer: $126272.71)
Rutherford Hayes has borrowed $80000 as mortgage loan at 7.5% interest rate and 30-year term. He has to pay the loan in monthly installments. After how many payments will the unpaid balance become $40000? (Answer: 264.94 months)
You have borrowed $56000 as a mortgage loan to buy a house. The bank will charge interest at the rate of 9% annually and requires a minimum monthly payment of $500. At the end of five years, you must pay off the entire mortgage by a “balloon payment”. You plan to pay only the minimum amount each month and then pay off the loan with the final payment. Find this balloon payment. (Answer: $49966.07)
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