Alliance Form 3 P1 Q4 — Currency Exchange (Buying vs Selling Rates)

KCSE (Form 3) Form 3 Numbers

Published

The Question

“A company receives US $100,000. It first changes the money into Kenya shillings and later converts the shillings into British pounds to buy a car. The bank quotes two rates for each currency, a buying rate and a selling rate. For the dollar the buying rate is 77.24 and for the pound the selling rate is 122.27. (a) Calculate the amount the company receives in Kenya shillings. (b) Calculate the amount the company gets in pounds, giving your answer to the nearest pound.”

1

Understand buying and selling rates

Each currency has two rates because the bank makes a small profit on every exchange. The bank uses its buying rate when you hand foreign currency over to it, and its selling rate when you want to buy foreign currency from it. Deciding which rate applies is the whole skill in this question.

Buying rate applies when foreign money comes into the bank; selling rate applies when foreign money leaves the bank.

2

Convert the dollars into shillings

The company brings dollars to the bank and asks for shillings, so from the bank's point of view it is buying those dollars. That means we use the dollar buying rate of 77.24. Multiply the rate by the number of dollars to get the amount in shillings.

77.24×100,000=7,724,000 shillings77.24 \times 100{,}000 = 7{,}724{,}000 \text{ shillings}
3

Convert the shillings into pounds

Now the company wants pounds to buy the car, so the bank is selling pounds to the company. That means we use the pound selling rate of 122.27. To move from shillings back to pounds we divide the shillings by this rate.

7,724,000122.27=63,171.7…\frac{7{,}724{,}000}{122.27} = 63{,}171.7\ldots
4

Round to the nearest pound

The question asks for the answer to the nearest pound, so we round the result. The first decimal is 7, which rounds up, giving 63,172 pounds.

63,171.7…≈£63,17263{,}171.7\ldots \approx \pounds 63{,}172

Final Result

The company first receives 7,724,000 Kenya shillings, which converts to 63,172 pounds to the nearest pound.

Why this method works

The two-rate system exists because a bank never exchanges money at a fair mid-price; it profits on the spread. When you deposit foreign currency the bank buys it low (buying rate), and when you take foreign currency out the bank sells it high (selling rate). Following the direction of the money tells you which rate to pick: dollars flowing in means the dollar buying rate, pounds flowing out means the pound selling rate. Multiplying converts from foreign currency into shillings, and dividing reverses the process from shillings back into a foreign currency.

✓

Reverse-check: 63,172 pounds x 122.27 = 7,724,041 shillings, which matches 7,724,000 shillings apart from the rounding up to the nearest pound.