Question

1. Construct an amortization schedule for a $1,000, 12% annual rate loan with 4 equal installments. What is the annual interest expense for the borrower, and the annual interest income for the lender, during Year 2?
2. Suppose on January 1 you deposit $1000 in an account that pays a nominal, or quoted, interest rate of 12%, with interest added (compounded) daily. How much will you have in your account on October 1, or 9 months later?
3. You want to buy a car, and a local bank will lend you $10,000. The loan would be fully amortized over 6 years (72 months), and the nominal interest rate would be 10%, with interest paid monthly. What is the monthly loan payment?
4. While Mary Corens was a student at the University of Tennessee, she borrowed $20,000 in student loans at an annual interest rate of 5%. If Mary repays $200 per year, then how long (to the nearest year) will it take her to repay the loan?

Answer 1

Question 1:

Loan Amount = PV = $1,000

r = interest rate = 12%

n = 4 installments

Installment Amount = [r*PV] / [1 - (1+r)^-n]

= [12%*$1,000] / [1 - (1+12%)^-4]

= $120 / 0.364481922

= $329.234436

= $329.23

Annual Interest expense for borrower and annual interest income for lender for year 2 is $94.89

Question 2:

n = number of days = October 1 - January 1 = 273 days

r = daily interest rate = 12%/365 = 0.0328737123%

Initial Investment = P = $1,000

Balance in Account after 9 months = P * (1+r)^n

= $1,000 * (1+0.0328737123%)^273

= $1,000 * 1.09388924

= $1,093.88924

Therefore, balance in account on October 1 is $1,093.89

Question 3:

Loan Amount = PV = $10,000

r = monthly interest rate = 10%/12 = 0.83333333%

n = 72 months

Monthly loan payment = [r*PV] / [1 - (1+r)^-n]

= [0.83333333% * $10,000] / [1 - (1+0.83333333%)^-72]

= $83.3333333 / 0.449822081

= $185.258432

Therefore, Monthly loan payment is $185.26

Question 4:

Loan Amount = PV = $20,000

Yearly Loan Payment = P = $200

Annual Interest rate = r = 5%

Yearly loan Payment = [r*PV] / [1 - (1+r)^-n]

$200 = [5% * $20,000] / [1 - (1+5%)^-n]

1 - (1+5%)^-n = 5

It will never be repaid since the interest amount per year amounts to $1,000 which is greater than the repayment. The difference adds up to the original amount and will result in the highest amount with the period of time