Question

For the next 10 questions, express monetary answers to the nearest whole dollar. For example, $1,234,567 (don’t include the cents) is appropriate for a monetary answer. Express the percentage in Questions 18 and 19 to the nearest hundredth.

16. A small business owner visits her bank to ask for a loan. The owner states that she can repay a loan at $3,000 per month for the next 5 years and then $4,000 per month for another 3 years after that. If the bank is charging customers 5.76% APR, how much would it be willing to lend the business owner?

17. Terrence purchases a house for $235,000 by getting a mortgage for $211,500 and paying a down payment of $23,500. It is a 20-year mortgage with a 3.92 percent interest rate and Terrence makes a payment at the end of each month. Suppose the house appreciates at a 2.25 percent rate per year. If equity is the value of the house minus how much is owed on the house, then how much equity does Terrence have at the end of ten years?

18. What is the interest rate of a 6-year, monthly $625 annuity due with a present value of $37,654?

19. After saving diligently her entire career, Terrence is ready to retire with a nest egg of $672,500. She needs to invest this money in a mix of stocks and bonds that will allow her to withdraw $5,850 per month for 20 years. What annual interest rate (APR) does she need to earn?

20. Bradley borrowed $72,500 in student loans and he has just graduated from Elon University. He earns enough at his new job to allow him to pay $575 per month on the loan. If the annual rate on the student loan is 4.38% (compounded monthly), how long will it take Bradley to pay off his student loans? Specify the number of months to the nearest whole number.

Answer 1

16. Loan Terms and Condition

Installments of $3000/ month for 5 years and $4000/ month for another 3 years

The APR is 5.76%

Since Installments are in month we have to find the monthly rate of interest

Monthly Rate of Interest = 5.76/12 = 0.48%

Finding the present Value of Installments

Loan Amount = 3000(P/A,0.48%,60)+4000(P/A,0.48%,36)(P/F,0.48%,60)

Loan Amount = 3000*52.025 + 4000*52.025*0.750

Loan Amount = 156075+156075

Loan Amount = $312150