Question

Give your answers to parts (b), (c) and (d) to the nearest whole number. Harinder has 14 000 US Dollars (USD) to invest for a period of five years. He has two options of how to invest the money. Option A: Invest the full amount, in USD, in a fixed deposit account in an American bank. The account pays a nominal annual interest rate of r%, compounded yearly, for the five years. The bank manager says that this will give Harinder a return of 17 500 USD. 1a. Calculate the value of r. [3 marks]

Answer 1

To calculate the interest rate, r, we need to use the compound interest formula. By substituting the given values into the formula and solving for r, we find that the interest rate is approximately 7%.

Step-by-step explanation:

To calculate the interest rate, r, we can use the formula:

Principal Amount * (1 + (r/100))^n = Final Amount

Where Principal Amount is the initial investment, Final Amount is the amount after five years, and n is the number of compounding periods.

In this case, the Principal Amount is $14,000, Final Amount is $17,500, and n is 5.

Substituting these values into the formula, we have:

$14,000 * (1 + (r/100))^5 = $17,500

Simplifying further, we get:

(1 + (r/100))^5 = 1.25

Take the fifth root of both sides:

1 + (r/100) = 1.25^(1/5)

Solve for r:

r/100 = 1.25^(1/5) - 1

r = (1.25^(1/5) - 1) * 100

Calculating the value of r, we get:

r ≈ 7.1035

Therefore, the interest rate, rounded to the nearest whole number, is 7%.

Answer 2

The annual interest rate (r) that Harinder earns from his investment, which grows to $17,500 in 5 years from an initial $14,000, calculated using the compound interest formula, is approximately 4.6% when rounded to the nearest whole number.

Step-by-step explanation:

Calculating the Annual Interest Rate (r)

To calculate the nominal annual interest rate (r) compounded yearly that Harinder would earn from his investment, we use the formula for compound interest:

A = P(1 + r/n)nt

Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money).
r = the annual interest rate (decimal).
n = the number of times that interest is compounded per year.
t = the time the money is invested for in years.

According to the question, Harinder's investment grows to $17,500 after 5 years from an initial investment of $14,000. The interest is compounded yearly (n=1). Thus:

$17,500 = $14,000(1 + r)5

To find r, we can rearrange the equation and solve for r:

1 + r = ($17,500 / $14,000)(1/5)

r = (($17,500 / $14,000)(1/5)) - 1

After solving, we find that the annual interest rate r is approximately 4.6%.