A principal of $4000 is invested at 8.75% interest, compounded annually. How many years will it take to accumulate $14,000 or more in the account?

Answer: 14.9 years, approximately 15years.

Step-by-step explanation:

Formular for finding the amount of a compound interest

A = P (1 + r/100) n

From the question given,

A = $14,000; P = $4,000; n = ? (year)

Rate = 8.75%.

Substitute for these values in the above equation, we therefore have

14,000 = 4,000 (1 + 8.75/100) n (is raised to the power of n)

Divide both side by 4,000

14,000/4,000 = 4,000 (1+8.75/100) n/4,000. solving the one in bracket fractionally

3.5 = { (100 + 8.75) / 100}n

3.5 = (108.75/100) n

3.5 = 1.0875n (raised to the power of n). In order to solve for 'n' to know the number of years, we take the logarithm of both side.

Log. 3.5 = Log (1.0875) n

Going by the law of logarithm,

Log 3.5 = nLog1.0875

Checking your log table, log 3.5 = 0.5441 and log1.0875 = 0.0364

Equating both and solve for n

0.5441 = 0.0364n

Divide through by the coefficient of n,

n = 0.5541/0.0364

n = 14.9 years

Approximately 15 years

Hence it will take $4,000 at 8.75% rate to amount to $14,000 a period of 14.9 years approximately 15years.