Cumulative level test: Scale, Leverage, and Containers: Arithmetic Before Decision

Check understanding, separately from reading

12 questions · 80% to pass · no timer. This longer test revisits both units in the level. These authored questions assess recognition and application of the taught distinctions, not professional qualification. You may review the lessons and retry. Repeat attempts reuse the question bank; a remembered answer is not proof of transfer to a new situation.

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Question 1

A savings brochure states that $10,000 invested at an assumed 7% a year for forty years will reach 'about $38,000', arrived at by multiplying 7% of the original by forty years. A reviewer checks the compounding and finds $149,744.58. The saver's goal was $60,000 for a specific purpose in forty years. What is the correct reading of the situation, and what single feature of the brochure's method caused the error?The goal is met with $89,744.58 to spare, and the error came from adding a constant dollar amount each year instead of multiplying the whole balance including prior growthThe goal is missed by $22,000, because the brochure's figure excludes the fees and taxes that a real account would charge over forty years

Question 2

A household wants a six-month reserve of $21,780 built from monthly transfers, while carrying a $12,000 balance at an assumed 24% on which the monthly interest is $240. It can direct $500 a month to one objective or the other, or split it. After a year of putting the whole $500 into transfers, what has the reserve reached, what interest accrued on the debt, and what is the honest way to compare the two uses of the same money?The reserve reaches $6,000 and no comparison is possible because the interest is a cost and the reserve is an asset, so the two cannot be placed on the same footingThe reserve reaches $6,000 of the $21,780 target and the debt accrues about $2,880 of interest if untouched, so the comparison is between the certain $240 a month of avoided interest and the liquidity the reserve buys

Question 3

A household's goal is $500,000 in twenty-five years, it currently holds nothing, and it has not decided whether the figure is nominal or real. At an assumed 2.5% inflation, what does the choice change about the required monthly contribution?It changes the target from $500,000 in today's purchasing power to $926,972.05 in the dollars of the target date, with the required contribution differing accordingly at a stated real rateIt changes nothing about the contribution, because inflation affects the value of the accumulated money and the goal by the same proportion over the same period

Question 4

A card carries $3,000 against a $6,000 limit. The holder pays down $1,500 and holds the rest, and separately receives a paid offer to 'improve' the account's profile. Which changes are computable facts, and which are unverifiable claims?Utilisation moves from 50.0% to 25.0% and a lower utilisation raises the score by a knowable amount once the reporting company's model is namedUtilisation moves from 50.0% to 25.0% and the interest saved is computable; any claim about a specific number of score points is unverifiable because models and versions differ and their weights are not published computeably

Question 5

A household is choosing between two mortgage-rate outcomes on an assumed $300,000 thirty-year loan: 6.5%, costing $1,896.20 a month and $382,633.47 of interest, against 6.0%, costing $1,798.65 and $347,514.57. In the same month, a ten-year buy-or-rent comparison under stated assumptions puts ownership ahead by only $2,755.44. What does placing the two numbers side by side show?The $35,118.90 lifetime difference in borrowing cost is more than twelve times the entire ten-year ownership margin, so the price of credit can outweigh the tenure questionThe two numbers are unrelated, because one concerns borrowing cost and the other concerns tenure, and combining them double-counts the effect of rates

Question 6

A household is deciding whether to buy or to keep renting, and has run the ten-year comparison. Its expected tenure is uncertain: there is a chance it moves in three years. Under the stated assumptions, ownership is behind at year two by $24,184.40, behind at year five by $19,962.87, behind at year eight by $9,060.16, ahead at year ten by $2,755.44 and ahead at year fifteen by $52,696.20. What should the household do with that information?Choose ownership anyway, because the comparison is favourable in the long run and a three-year move is a low-probability event that can be ignoredTreat the horizon as the decisive input, note that early exit is dominated by transaction costs and interest, and price the cost of a mistaken move before deciding

Question 7

A worker earns $5,000 a month and receives a 3% nominal increase while inflation runs at 2.5%. The employer's withholding is computed on the new nominal pay. What is the real value of the increase, and what does the withholding arrangement imply about the relationship between tax and inflation?The increase is worth $5,024.39 in real terms, a real gain of about 0.49%, while withholding and any income tax computed on the nominal amount take a share of the whole nominal increaseThe increase is worth $5,150 in real terms, because withholding is computed after adjusting wages for inflation by the annual adjustment to the standard deduction

Question 8

A worker defers 6% of a $5,000 monthly gross into an employer plan, which is $300 a month, and is in an assumed 22% marginal income tax bracket. Payroll taxes are $382.50 a month, unchanged. After thirty years at an assumed 6% annual return, what has the deferral stream become, and what did the election fail to reduce?An annual deposit of $3,600 for thirty years at 6% becomes $284,609.47, and the election reduced both income tax and payroll taxes by the marginal rateAn annual deposit of $3,600 for thirty years at 6% becomes $284,609.47, and the election did not reduce payroll taxes, which are computed on wages before most deferrals

Question 9

A household with a three-month reserve of $10,890 faces a $10,000 emergency. Withdrawing from a retirement container would cost an assumed 22% in income tax plus an assumed 10% early-distribution tax. It could also rebuild the reserve instead. What is the arithmetic comparison?The withdrawal costs about $3,200 on $10,000, whereas the reserve's annual opportunity cost in the stated illustration was about $130.68, which is the reason a small reserve is cheap insurance against a taxable withdrawalThe withdrawal costs about $2,200 on $10,000, since the early-distribution tax replaces the income tax rather than being charged in addition to it

Question 10

A saver can commit $7,000 a year of pre-tax resources for thirty years at an assumed 6% return. Her marginal rate this year is 12%. She expects the rate at withdrawal to be 32%. A colleague says the choice between a tax-deferred container and a Roth container does not matter because the rates are just timing. What does the arithmetic show?The tax-deferred container wins here: it accumulates $553,407.30 and the deferral always beats paying tax early, whatever the later rateThe Roth wins here: contributing after tax at 12% gives $486,998.43 tax-free, against $376,316.97 after tax from the tax-deferred container at a 32% withdrawal rate

Question 11

A household treats a $600 monthly contribution as '12% of income' because gross pay is $5,000 a month. After payroll taxes of $382.50 and illustrative federal withholding of $418.33, net pay is $4,199.17. What is the correct statement of the saving rate, and what does the difference reveal about a plan built on gross income?The contribution is 12.0% of gross and 14.29% of net, so a plan written on gross income understates the share of take-home pay that must be committedThe contribution is 14.29% of gross and 12.0% of net, so the plan written on gross income understates the burden

Question 12

A one-page plan states: contribute $600 a month, assume 9% a year, and reach $500,000 in twenty-five years. It holds no reserve, carries a $12,000 balance at an assumed 24%, and names no review date. Under an assumed 5% return the contributions produce $357,305.83, and reaching $500,000 on $600 a month would need about 7.18% a year. Which finding should be reported first, and why?The missing reserve is the first finding, because no plan can be evaluated until a shock is modelled and every other figure depends on itThe plan fails on its own terms even if nothing goes wrong: the return assumption is doing the work, and the debt alone consumes $2,880 a year against $7,200 of contributions

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