Answer: 14.9 years, approximately 15years.
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.