Question

William bought stock for $100,000. He expects the stock to increase in value at a rate of 6% compounded monthly for the next 5 years. How much is the stock expected to be worth at the end of the 5th year?

Answer 1

To calculate the future value of the stock after 5 years with monthly compounding interest, we can use the formula for compound interest:

A = P * (1 + r/n)^(n*t)

Where:

A = Future value

P = Principal amount (initial investment)

r = Annual interest rate (as a decimal)

n = Number of times interest is compounded per year

t = Number of years

Using the given values:

P = $100,000

r = 6% = 0.06 (as a decimal)

n = 12 (monthly compounding)

t = 5 years

Plugging these values into the formula, we get:

A = $100,000 * (1 + 0.06/12)^(12*5)

Calculating the exponent:

A = $100,000 * (1.005)^(60)

Using a calculator or spreadsheet, we can compute the value inside the parentheses raised to the power of 60:

A ≈ $100,000 * 1.348561533

A ≈ $134,856.15

Therefore, the stock is expected to be worth approximately $134,856.15 at the end of the 5th year.