Question

Your financial advisor/cousin has told you about an investment that will ABSOLUTELY go up in value over a 7-year period. He claims that for every dollar you invest, your balance will increase to $3 over that period of time. What annual interest rate (assume annual compounding) is he claiming you will receive? Enter your answer as a number with 2 decimals and no percentage sign. For example, if your answer is 13.45% - you should enter 13.45. Do not enter the answer in the form of 0.1345. Answers in that format will receive at least a 1 point deduction.

Answer 1

To calculate the annual interest rate, we can use the compound interest formula and solve for r. The annual interest rate he claims you will receive is approximately 0.1855, or 18.55%.

Step-by-step explanation:

To calculate the annual interest rate, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

• A is the final account balance ($3)
• P is the principal amount invested ($1)
• r is the annual interest rate (what we want to find)
• n is the number of times interest is compounded per year (assume once annually)
• t is the number of years (7)

Plugging in the values, we have:

3 = 1(1 + r/1)^(1*7)

3 = (1 + r)^7

(1 + r)^7 = 3

To solve for r, we need to take the seventh root of both sides:

1 + r = 3^(1/7)

1 + r ≈ 1.1855

r ≈ 0.1855

So, the annual interest rate he claims you will receive is approximately 0.1855, or 18.55%.