Question

If $7,500 is placed in a savings account with a 5.5% nominal interest rate compounded monthly, how many years will it take for the investment to reach $10,000?

a) 4 years
b) 5 years
c) 6 years
d) 7 years

Answer 1

To determine the number of years required for $7,500 to grow to $10,000 with a 5.5% interest rate compounded monthly, we use the compound interest formula. After plugging in the values and solving for time, we find that it will take approximately 6.116 years, which rounds to option c) 6 years.

Step-by-step explanation:

To calculate how many years it will take for an investment of $7,500 to grow to $10,000 with a 5.5% nominal interest rate compounded monthly, we use the formula for compound interest:

A = P(1 + r/n)nt

Where:

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

To find t, we rearrange the formula:

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

Now plug in the values:

P = $7,500

A = $10,000

r = 5.5% or 0.055

n = 12 (since interest is compounded monthly)

Calculate t:

t = (log(10000/7500)) / (12 * log(1 + 0.055/12))

t ≈ 6.116 years

The closest full year answer to the calculated time is option c) 6 years.