Mathematics
- (Problem 26.1) Smith receives $400 in 1 year, $800 in 2 years, $1,200 in 3 years and so
on until the final payment of $4,000. Using an effective interest rate of 6%, determine
the present value of these payments at time 0. - (Problem 26.21) A perpetuity costs 77.1 and makes annual payments at the end of the
year. The perpetuity pays 1 at the end of year 2, 2 at the end of year 3, . . . , n at the
end of year (n+1): After year (n+1), the payments remain constant at n. The annual
effective interest rate is 10.5%. Calculate n. - (Problem 26.27) The present value of a 25-year annuity-immediate with a first payment
of 2500 and decreasing by 100 each year thereafter is X. Assuming an annual effective
interest rate of 10%, calculate X. - (Problem 37.4) Julie bought a house with a 100,000 mortgage for 30 years being repaid
with payments at the end of each month at an interest rate of 8% compounded monthly.
What is the outstanding balance at the end of 10 years immediately after the 120th
payment? - (Problem 37.9) A loan is being repaid with 20 payments of 1,000. The total interest
paid during the life of the loan is 5,000. Calculate the amount of the loan. - (Problem 37.15) A 20-year loan of 1,000 is repaid with payments at the end of each
year. Each of the first ten payments equals 150% of the amount of interest due. Each
of the last ten payments is X. The lender charges interest at an annual effective rate
of 10%. Calculate X.
Hint for #6: It’s a bit annoying to calculate the amounts of the first 10 payments.
Instead, you can reason in this way–at each time, the payment is 150% of the interest
due. Then 50% of the payment is used to reduce the principal. If the loan balance at
time t is Bt
, then the interest payment is 0.1Bt and the loan payment is then 0.05Bt
.
Therefore, the principal is reduced by 5% with each of the first 10 payments. You can
then calculate the loan balance at t = 1
Sample Solution
Atomic power, the energy representing things to come of the 1950s, is presently beginning to feel like the past. Around 450 atomic reactors overall right now produce 11% of the world power, or roughly 2500 TWh in a year, simply under the complete atomic power created universally in 2001 and just 500 TWh more than in 1991. The quantity of working reactors overall has seen a similar stagnation, with an increment of just 31 starting around 1989, or a yearly development of simply 0.23% contrasted with 12.9% from 1959 to 1989. Most reactors, particularly in Europe and North America, where worked before the 90s and the typical time of reactors overall is a little more than 28 years. Enormous scope atomic mishaps, for example, Chernobyl in 1986 or, considerably more as of late, Fukushima in 2011 have harmed public help for atomic power and aided cause this decay, yet the heaviness of proof has progressively recommended that atomic is more secure than most other energy sources and has an extraordinarily low carbon impression, causing the contention against atomic to move from worries about wellbeing and the climate to inquiries regarding the financial feasibility of atomic power. The pivotal inquiry that remains is subsequently about how well atomic power can contend with renewables to deliver the low carbon energy expected to handle an unnatural weather change. The expenses of most environmentally friendly power sources have been falling quickly and progressively ready to outcompete atomic power as a low carbon choice and, surprisingly, petroleum derivatives in certain spots; photovoltaic boards, for instance, have split in cost from 2008 to 2014. More awful still for atomic power, it appears to be that while expenses of environmentally friendly power have been falling, plans for new atomic plants have been tormented with delays and extra expenses: in the UK, Hinkley Point C power station is set to cost £20.3bn, making it the world’s most costly power station, and huge issues in the plan have brought up issues regarding whether the plant will be finished by 2025, it’s ongoing objective. In France, the Flamanville 3 reactor is presently anticipated to cost multiple times its unique spending plan and a few postponements have pushed the beginning up date, initially set for 2012, to 2020. The story is similar in the US, where deferrals and additional expenses have tormented the development of the Vogtle 3 and 4 reactors which are currently because of be finished by 2020-21, 4 years over their unique objective. Atomic power apparently can’t convey the modest, carbon free energy it guaranteed and is being outflanked by sustainable power sources, for example, sun based and wind. The urgent and repeating issue with atomic power is that it requires tremendous forthright expenses, particularly when plants are fabricated separately, and can just a brief time after the beginning of development. This implies that interest into atomic is unsafe, long haul and isn’t possible well on a limited scale, however new advances like SMRs (Little Measured Reactors) may change this in the next few decades, making it a lot greater bet. Enhancements in different innovations over the timeframe an atomic plant is fabricated implies that is in many cases better for private firms, who are less inclined to have the option to bear the cost of enormous scope p>
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