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# Accounting: Monthly Interest Rates

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Love Canal General Hospital wants to purchase a new blood analyzing device today. Its local bank is willing to lend it the money to buy the analyzer at a 3 percent monthly rate. The loan payments will start at the end of the month and will be \$1,600 per month for the next eighteen months. What is the purchases price of the device?

Dr. Thomas plans to retire today and would like an income of \$ 400,000 per year for the next fifteen years with the income payments starting one year from today. He will be able to earn interest of 8 percent per year compounded annually from his investment account. What must he deposit today in his investment account to achieve this income of \$ 400,000 per year?

Carondelet Hospital is evaluating a lease arrangement for its ambulance fleet. The total value of the lease is \$420,000. The hospital will be making equal monthly payments starting today.

Questions:
a. What is the monthly interest rate if the lease payments are \$24,000 per month for twenty-four months?
b. What is the monthly interest rate if the lease payments are \$24,000 per month for thirty-six months?
c. What is the monthly interest rate if the lease payments are \$30,000 per month for for thirty-six months?

#### Solution Summary

This solution illustrates how to use Excel functions to find the purchase price of an asset based on its monthly payments, the annual amount a person will have if they draw down a deposit over several years, and the interest rate implicit in a lease.

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## A) What annual interest rate did the man pay? B) How much would the man need to repay at the end of two months if he borrowed \$5000 with the same rules and same annual interest rate?

1. Three students each have \$1000 to invest from their summer jobs. Armen invests his money in an account that earns simple interest at an APR of 5 percent. Barok invests his money in an account that earns 4.9 percent interest per year compounded annually. Carrie invests her money in an account that earns 4.8 percent interest per year compounded monthly. Find how much money each student has in his or her account after
A) 2 years
B) 10 years
C) 30 years

2. Here's an old story: A man walks into a New York City bank and asks for a \$5000 loan, offering his Ferrari, worth \$250,000 as collateral. He tells the loan officer that he needs the money for two weeks for an important venture. The loan officer, having the car as security and after checking references, gives the man the money he requested, with a signed agreement that he will pay the money plus \$45 in interest when he returns in two weeks. The bank officer takes the car keys and the car is parked in the bank's underground lot. The man returns in exactly two weeks, pays the loan and interest, and reclaims his car. The bank officer asked him why he was willing to pay such a high interest rate. His reply: where else can I safely park my car for two weeks in New York City for only \$45?
A) What annual interest rate did the man pay?
B) How much would the man need to repay at the end of two months if he borrowed \$5000 with the same rules and same annual interest rate?

6. A new parent wants to have \$80,000 in a college savings account in 18 years. Although it's difficult to predict what the APR will be over 18 years, we can get a sense of how much the parent should save each month using various assumptions. Calculate the monthly savings needed if the money is invested in an account with monthly compounding and an APR of
A) 4 percent
B) 7 percent
C) 9 percent

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