question about interest rates

Question

Rob has the opportunity to invest in two different Project Finance projects. The first project is a railroad that will pay monthly interest of $100.00 for 3 years, with a one-year grace period (there is no interest payment in this period) and in the last month, in addition to the interest, there will be an additional payment of $500.00. The other investment is a debenture of a sanitation company that works in bullet format, interest and amortization are paid together once at the end of the debenture, and will pay $3500 at the end of the third year. Assuming an interest rate of 11% per year, what alternative contains the present value of both investments?

a) $3.101,90; $2.559,17

b) $257,12; $2.559,17

c) $3.494,30; $2.629,60

d) $3.774,05; $3.023,43

e) $3.547,00; $2.702,64

Answer 1

The correct answer is A: $3,101.90 and $2,559.17.

For the railroad investment, there is a one-year grace period followed by 36 monthly payments of $100, plus an additional $500 in the final month. Using the equivalent monthly interest rate of ((1.11)^(1/12))-1), or approximately 0.8735%, we discount all payments back to today. This gives a present value of $3,101.90.

For the sanitation company's debenture, the entire $3,500 is paid at the end of three years. Its present value is calculated as:

PV=(3500)/(1.11)^3=$2,559.17

Therefore, option A is correct, assuming the railroad's three years of payments begin after the one-year grace period.