The table below shows the rand equivalent of one British pound and one US dollar.
| COUNTRY | CURRENCY | RATE OF EXCHANGE OF THE RAND |
|---|---|---|
| Britain (United Kingdom) | Pound (£) | 21.41 |
| United States of America | Dollar ($) | 13.45 |
A South African nurse works in the United States of America.
4.2.1 The nurse saves the equivalent of R4 800 per month. Calculate the amount, in US (American) dollars, that she saves per month.
4.2.2 She ordered a book from the United Kingdom (Britain) and paid $85 for it. Calculate the price of the book in pounds (£).
4.3 A sum of money doubles in 5 years when the interest is compounded annually. Calculate the rate of interest.
Answer (2)
Converts the nurse's savings from R4800 to US dollars: 13.45 4800 = 356.88 .
Converts the price of the book from 85 t o B r i t i s h p o u n d s : \frac{85 \times 13.45}{21.41} = 53.40$.
Calculates the annual interest rate for a sum of money to double in 5 years: 2 5 1 − 1 = 0.1487 .
States the final answers: The nurse saves $\boxed{ 356.88} , the book costs £53.40 , and the annual interest rate is 14.87% .
Explanation
Problem Analysis We are given the exchange rates between the South African Rand (R), the British Pound (£), and the US Dollar ($). We need to calculate the nurse's savings in US dollars, the price of the book in British pounds, and the annual interest rate for a sum of money to double in 5 years.
Calculating Savings in USD To find the nurse's savings in US dollars, we need to convert R4800 to USD. We know that 1 = R 13.45 , so we can divide the amount in Rand by the Rand equivalent of one US dollar: U S D = 13.45 R 4800 = R 356.88
Calculating Price in GBP To find the price of the book in British pounds, we first convert the price from USD to Rand and then from Rand to GBP. We know that 1 = R 13.45 and £1 = R21.41. So, we have: P r i c e R an d = 85 × 13.45 = R 1143.25 P r i c e GBP = 21.41 R 1143.25 = £53.40
Calculating Annual Interest Rate To calculate the annual interest rate, we use the compound interest formula: A = P ( 1 + r ) n , where A is the amount after n years, P is the principal amount, r is the annual interest rate, and n is the number of years. Since the sum doubles in 5 years, we have A = 2 P and n = 5 . Substituting these values into the formula, we get: 2 P = P ( 1 + r ) 5 Dividing both sides by P, we get: 2 = ( 1 + r ) 5 Taking the fifth root of both sides, we get: 2 5 1 = 1 + r Solving for r, we get: r = 2 5 1 − 1 r ≈ 1.1487 − 1 = 0.1487 So the annual interest rate is approximately 14.87%.
Final Answer The nurse saves approximately $356.88 per month. The price of the book is approximately £53.40. The annual interest rate is approximately 14.87%.
Examples
Understanding exchange rates is crucial for international transactions, such as when a South African nurse working in the USA wants to send money home or purchase goods from another country. Similarly, calculating compound interest is essential for understanding investments and loans. For instance, if you invest money in a savings account with compound interest, you can calculate how long it will take for your investment to double. These calculations are useful in personal finance and business.
The nurse saves approximately $356.88 per month, the book costs about £53.40, and the annual interest rate is approximately 14.87%.
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