02 May Question: 2. [Theory] For the following questions, the present is Year 0, and the relevant interest rate is…
2. [Theory] For the following questions, the present is Year 0, and the relevant interest rate is 10% per year. Round your answers to the nearest cent. Show your work, or you will not receive marks. There’s a formula sheet at the end of the assignment.
a. (2 marks) Use (P/F,i,N) to find the present value (Year 0 value) of $1,000 in Year 10.
Present Value: $ _______________
b. (4 marks) Maintenance costs for a machine are $100 in Year 1, after which they go up by $50 a year. Thus, costs are $150 in year 2, $200 in Year 3, etc. The last maintenance costs are incurred in Year 30. Use (P/A,i,N) and (A/G,i,N) to find the present value (Year 0 value) of these maintenance costs.
Present Value: $ _______________
c. (4 marks) An after-school sports program for disadvantaged children provides benefits worth $500 in Year 1. Each year after that, the benefits from the program go up by 10%, so they are $550 in Year 2, $605 in Year 3, etc. The last year in which benefits are provided is Year 20. Use (P/A,g,i,N) (or equivalently, (P/A,io,N)/(1+g) ) to calculate the present value of these benefits.
Present Value: $_____________
d. (2 marks) You want to save up $1,000,000 by the time you retire in Year 45. Use (A/F,i,N) to calculate how much money you must put in a bank account every year, starting in Year 1 and with the last payment being in Year 45, in order to have $1,000,000 in Year 45.
Annual Payment: $______________
| (F/P,i,N) = (1+i)N | (P/F,i,N) = (1+i)−N | (A/F,i,N) = i(1+i)N−1 |
| (F/A,i,N) = [(1+i)N−1]i | (A/P,i,N) = i(1+i)N(1+i)N−1 | (P/A,i,N) = (1+i)N−1i(1+i)N |
| (A/G,i,N) = 1i−N(1+i)N−1 | (P/A,g,i,N) = (PA,io,N)⁄1+g | io=1+i1+g−1 |
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