Question

1-What should an investor pay for an investment property promising a $200,000 return after 10 years if a 7% annual return (compounded annually) on investment is projected?

2-Given the following information on a 30-year fixed-payment fully-amortizing loan, determine the remaining balance that the borrower has at the end of five years. Interest Rate: 4%, Monthly Payment: $3,000

3-An investor has an opportunity to invest in a rental property that will provide net cash returns of $2,000 per month for 10 years, at which point it can be sold for $400,000. The investor believes that an annual return of 10% should be earned on the property. How much should be paid for the property?

4-A borrower would like to finance a property worth $1,000,000 for 30 years at 3% interest. The lender indicates that loan fees (origination and discount points) equal to 3% of the loan amount will be charged upfront to obtain the loan. What is the actual effective interest rate of the loan (annual rate of interest, compounded monthly) if the loan is repaid back in 20 years?

5-A buyer can afford no more than $1,200 per month in payments. The most favorable loan available in the market is a 30-year loan at 5%. What is the maximum affordable house with a 20% down payment?

Answer 1

Answer to Question 1:

Amount to be received in 10 years = $200,000
Interest rate = 7%

Present value = Amount to be received / (1 + Interest rate)^Period
Present value = $200,000 / 1.07^10
Present value = $101,669.86

So, an investor should pay $101,669.86 or $101,670 for this investment.

Answer to Question 2:

Monthly payment = $3,000
Annual interest rate = 4%
Monthly interest rate = 0.3333%
Remaining period = 25 years or 300 months

Loan outstanding = $3,000/1.003333 + $3,000/1.003333^2 + .... + $3,000/1.003333^299 + $3,000/1.003333^300
Loan outstanding = $3,000 * (1 - (1/1.003333)^300) / 0.003333
Loan outstanding = $3,000 * 189.46041
Loan outstanding = $568,381.23

So, remaining balance of loan is $568,381.23