BA1: Financial mathematics

Answer: D. A financial intermediary links savers (those with surplus funds) and borrowers, transforming deposits into loans and managing risk, maturity and liquidity in the process. Setting economy-wide interest rates and issuing currency are functions of the central bank, and collecting taxes is a government function. The intermediation role — bringing together the two sides of the market — is what defines a commercial bank's core activity.

Answer: D. Acting as lender of last resort — providing liquidity to banks in difficulty to maintain financial stability — is a classic central bank function. A central bank's aim is economic and financial stability, not private profit. It deals with banks and government rather than offering retail current accounts to the public. Setting corporation tax is a government (fiscal) function, not a central bank one.

Answer: B. Compound interest applies the rate to the accumulating balance each year: future value = £5,000 × (1.06)³ = £5,000 × 1.191016 = £5,955 (to the nearest £). The £5,900 figure is simple interest, which applies 6% to the original £5,000 each year (£5,000 + 3 × £300); the difference is the interest earned on previous interest — the essence of compounding. The £5,300 figure applies only one year's interest.

Answer: C. Present value discounts a future sum back to today: PV = £10,000 ÷ (1.10)² = £10,000 ÷ 1.21 = £8,264 (to the nearest £). The £8,000 answer deducts a flat £1,000 per year, treating discounting like simple interest. The £9,091 answer discounts for only one year (£10,000 ÷ 1.10). The £8,116 answer discounts for three years. The exponent must match the number of years until the cash flow is received.

Answer: A. The present value of a perpetuity (a constant cash flow continuing indefinitely) is the annual cash flow divided by the discount rate: £2,000 ÷ 0.08 = £25,000. The £16,000 answer multiplies by the rate instead of dividing. The £2,160 answer adds one year's interest to the cash flow. The £250,000 answer divides by 0.008 rather than 0.08 — a decimal-place error. Dividing the cash flow by the rate is the key relationship.

Answer: B. When sterling strengthens, each pound buys more dollars, so a UK exporter's goods priced in sterling translate into a higher dollar price for US buyers. This makes the goods less competitive and tends to reduce export volumes. Goods becoming cheaper for US customers would be the effect of a weaker pound, not a stronger one. There is certainly an effect on the price US customers pay, because exchange rates feed directly into the foreign-currency price; and a stronger pound makes US imports cheaper for the UK firm, not more expensive.

Answer: B. Liquidity refers to how quickly and cheaply an asset can be converted into cash without loss of value. Cash in a current account is already money and so is the most liquid. A ten-year bond and shares in an unlisted company can be harder to sell at short notice, and commercial property is notably illiquid — it can take months to sell. Managing liquidity means balancing the return on less liquid assets against the need for ready cash.

Answer: D. Credit creation describes how banks lend out a proportion of the deposits they hold; that lending is re-deposited and lent again, multiplying the money supply well beyond the original deposit. Quantitative easing is a central bank asset-purchase programme, fiscal expansion is a government taxation-and-spending action, and currency devaluation concerns the exchange rate — none captures the commercial-bank lending multiplier.

Answer: B. To convert dollars into sterling, divide by the dollars-per-pound rate: $24,000 ÷ 1.60 = £15,000. Multiplying instead ($24,000 × 1.60 = $38,400) would convert sterling into dollars — the wrong direction. £14,400 deducts 40% from the dollar amount ($24,000 × 0.60) and £25,600 adds $1,600 to it; neither is a currency conversion. The rule is to divide by the rate when moving from the quoted currency (here, dollars) back to the base currency (sterling).

Answer: C. The effective annual rate compounds the monthly rate over 12 months: (1.02)¹² − 1 = 1.2682 − 1 = 0.2682, or 26.8%. The 24.0% answer simply multiplies 2% by 12, ignoring the compounding of interest on interest. Options B and D are unsupported. Because interest is charged monthly on a rising balance, the true annual cost exceeds the simple 24% figure — the difference is the effect of compounding.

Answer: D. Higher interest rates raise the cost of borrowing and increase the return on saving, so firms tend to invest less and consumers tend to spend less and save more — dampening aggregate demand. This is the usual transmission mechanism of tighter monetary policy. Cheaper borrowing that encourages spending would be the effect of a rate cut. The claim that the exchange rate always immediately falls reverses the typical effect, and rising inflation is the opposite of the anti-inflationary aim of a rate rise.

Answer: A. A forward exchange contract lets the company agree today the rate at which it will convert the future dollar receipt, removing the uncertainty of exchange-rate movements over the three months. Futures and options can serve a similar hedging purpose. The other options are unrelated to currency risk: advertising, tax payments and share issues do nothing to protect the sterling value of a future foreign-currency cash flow.

Answer: A. Discount each inflow and subtract the initial outlay. Year 1: £6,000 × 0.909 = £5,454. Year 2: £6,000 × 0.826 = £4,956. Present value of inflows = £10,410. NPV = £10,410 − £10,000 = £410. The positive NPV suggests the project is worthwhile. The £2,000 answer is the undiscounted net cash flow, ignoring the time value of money. The £10,410 answer omits the initial investment. £210 does not follow from the stated discount factors.

Answer: D. An annuity factor discounts a stream of equal annual cash flows in a single step: present value = £2,000 × 2.487 = £4,974. The £6,000 answer is the undiscounted total of the three receipts, ignoring the time value of money. The £6,621 answer compounds rather than discounts. The annuity factor already sums the individual discount factors for years 1 to 3, so it is applied once to the annual amount. £1,653 discounts a single £2,000 receipt for two years (£2,000 ÷ 1.10²) instead of valuing the three-year stream.

Answer: C. Money markets deal in short-term instruments of high liquidity, such as treasury bills, which mature within a year. Capital markets deal in long-term finance — equities and long-dated bonds, which fund longer-term investment. Long-term corporate bonds, ordinary shares and long-term government bonds are therefore all capital-market instruments. The distinguishing feature of the money market is the short maturity of what is traded.

Answer: A. To convert euros into sterling, divide by the euros-per-pound rate: €30,000 ÷ 1.20 = £25,000. The £36,000 answer multiplies by 1.20, which would convert sterling into euros — the wrong direction. The rule is to divide by the rate when moving from the quoted currency (euros) back to the base currency (sterling). A stronger pound would make these imports cheaper in sterling; a weaker pound, more expensive. £24,000 deducts 20% from the euro amount instead of dividing by 1.20, and £25,500 deducts 15%; neither is a currency conversion.

Answer: D. Quantitative easing is a monetary policy tool in which the central bank creates new money electronically to buy financial assets, mainly government bonds, increasing liquidity in the financial system and supporting lending and demand. Raising income tax and cutting public spending are fiscal measures controlled by the government, and imposing tariffs is a trade policy. Quantitative easing operates through the central bank's balance sheet, not through taxation or spending.

Answer: D. The IRR is the discount rate at which the present value of a project's cash inflows equals the present value of its outflows — that is, the rate at which net present value is zero. A project is generally acceptable if its IRR exceeds the company's cost of capital. Confusing the IRR with total accounting profit, with the expected inflation rate, or with the bank's interest rate are all common errors; none of these defines the IRR, although the cost of capital is the benchmark it is compared against.

Answer: B. Present value = future cash flow × discount factor = £8,000 × 0.794 = £6,352. The discount factor, which is less than 1, reduces the future sum to its worth today, reflecting the time value of money. The value £10,076 divides by the factor instead of multiplying, which would compound rather than discount. The £8,000 figure ignores discounting altogether. Multiplying the cash flow by the factor is the correct step. £7,206 subtracts 794 from £8,000, treating the factor as a deduction rather than a multiplier.

Answer: C. Simple interest is charged only on the original principal: interest = £4,000 × 5% × 3 = £600, so the total is £4,000 + £600 = £4,600. The value £4,630 would result from compounding, which is not used here. £4,200 applies only one year's interest. Simple interest gives a constant annual amount, unlike compound interest, which would earn interest on accumulated interest. £12,600 multiplies the principal by the three years before adding the interest.

Answer: D. An issue of ordinary shares raises permanent, long-term finance, as equity has no repayment date. An overdraft, trade payables and a six-month loan are all short-term sources used to fund working capital and day-to-day operations. Matching the term of finance to the term of the assets it funds — long-term finance for long-term assets — is a basic principle of sound financial management.

Answer: B. Purchasing power parity adjusts the rate by the ratio of the two inflation rates: expected rate = $2.00 × (1.10 ÷ 1.00) = $2.20. Higher US inflation means more dollars are needed per pound, so the dollar weakens to $2.20. The figure $1.82 inverts the ratio, which would imply the dollar strengthening despite higher US inflation. The currency with the higher inflation rate is expected to depreciate. $1.80 deducts 10% from the rate, moving it in the wrong direction, and $2.10 applies only half of the 10% inflation differential.

Answer: A. When a central bank buys government bonds, it pays banks with newly created money, increasing their reserves and their capacity to lend — expanding the money supply (open-market operations and quantitative easing work this way). Selling bonds drains money from the system. Raising reserve requirements and increasing interest rates both tend to reduce lending and the money supply. Buying assets injects money; selling assets withdraws it.

Answer: D. An interest rate swap lets the company exchange its variable-rate obligation for a fixed-rate one, removing the risk that rising rates increase its payments; forward rate agreements and interest rate futures serve a similar purpose. Issuing shares, spending more on advertising and holding more inventory do nothing to manage interest rate risk. Hedging matches a financial instrument to the specific risk being faced.

Answer: A. Present value of the inflows = £5,000 × 3.791 = £18,955. Net present value = £18,955 − £20,000 = −£1,045. The negative NPV suggests the project should be rejected, as it does not recover its cost in present-value terms. The figure £18,955 omits the initial investment, and £1,045 has the wrong sign. The annuity factor discounts the whole stream of equal cash flows in one step.

Answer: D. Compound interest applies the rate to the growing balance: £8,000 × (1.04)² = £8,000 × 1.0816 = £8,653 (to the nearest £). The figure £8,640 applies simple interest (£8,000 + 2 × £320). £8,320 adds only one year's interest. The small excess of £8,653 over the simple-interest figure is the interest earned in year two on year one's interest — the effect of compounding.

Answer: C. Interest rate parity holds that the currency with the higher interest rate trades at a forward discount, so that the interest-rate advantage is offset by an expected fall in the currency's value — otherwise riskless profit would be possible. A forward premium attaches to the lower-interest currency. The forward rate is not unchanged, and parity describes a market relationship rather than an official peg. Higher interest rate, forward discount.

Answer: A. A stock exchange provides an organised market where companies can raise long-term finance by issuing securities and where investors can buy and sell those securities, giving them liquidity. Setting interest rates and issuing currency are central bank functions, and collecting taxes is a government function. By enabling the issue and trading of shares and bonds, the exchange channels long-term capital to businesses.

Answer: B. With constant annual inflows, the payback period is the initial investment divided by the annual inflow: £40,000 ÷ £10,000 = 4 years. Payback measures how long it takes to recover the original outlay in cash terms; it ignores the time value of money and any cash flows after the payback point. The other figures do not match the £40,000 outlay recovered at £10,000 a year.

Answer: D. Raising interest rates increases the cost of borrowing and the reward for saving, cooling spending and demand and so helping to bring inflation down — the standard contractionary monetary response. Cutting rates, expanding the money supply and reducing reserve requirements are all expansionary measures that would tend to add to demand and inflationary pressure. Tackling inflation calls for tighter, not looser, monetary policy.

Answer: D. Present value = future cash flow × discount factor = £5,000 × 0.792 = £3,960. The discount factor of less than 1 reduces the future amount to its value today. The figure £6,313 divides by the factor instead of multiplying, which compounds rather than discounts, and £5,000 ignores discounting. Multiplying the future sum by the appropriate discount factor converts it to present value. £20,000 multiplies the receipt by the number of years rather than by the discount factor.

Answer: B. The effective annual rate compounds the quarterly rate over four quarters: (1.03)⁴ − 1 = 1.1255 − 1 = 0.1255, or 12.6%. The figure 12.0% simply multiplies 3% by four, ignoring the compounding of interest on interest within the year. Because interest is earned each quarter on a growing balance, the true annual rate exceeds the simple 12%. Compounding the periodic rate gives the effective annual figure. 6.0% compounds over only two quarters ((1.03)² − 1 = 6.1%) instead of four.

Answer: A. A forward rate is agreed today for a currency exchange that will be settled at a specified future date, allowing businesses to fix the rate in advance and hedge exchange rate risk. The rate for immediate delivery is the spot rate, a central bank's official rate applies to a fixed or managed regime, and a past average is a historical statistic. Locking in a future rate now is the essence of a forward.

Answer: C. When the domestic currency appreciates, each unit buys more foreign currency, so foreign-priced imports become cheaper in domestic-currency terms and import costs fall — a benefit to importers. Costs would rise if the currency weakened, and they are certainly affected by the exchange rate, so they are neither unchanged nor a barrier to importing. A stronger home currency lowers the home-currency cost of imports.

Answer: D. A positive net present value means the discounted value of the project's future cash inflows exceeds its initial cost, so it is expected to increase the wealth of the business and should, in principle, be accepted. NPV is based directly on cash flows, not profits, so it does not ignore them; and a value-adding project should not be rejected or deferred without reason. A positive NPV is the basic accept signal in investment appraisal.

Answer: B. Maturity transformation is the process by which banks convert short-term, liquid deposits into longer-term, less liquid loans — a core function of financial intermediation that also creates liquidity risk. Credit rationing is the limiting of lending, quantitative easing is a central bank asset-purchase programme, and currency hedging manages exchange rate risk. Turning short-term funds into long-term lending defines maturity transformation.

Answer: D. Compound interest: £2,000 × (1.10)³ = £2,000 × 1.331 = £2,662. The figure £2,600 applies simple interest (£2,000 + 3 × £200). £2,420 compounds for only two years, and £2,200 for one year. The amount by which £2,662 exceeds the simple-interest £2,600 is the interest earned on previously accumulated interest, which is what compounding captures.