Using the compound interest formula, the rate of interest at which the sum of money will become 6 times itself in 15 years compounded annually is 12.25%.
Where:
The amount of money accumulated after 15 years, including interest = A.
The principal amount (initial sum of money) = P
The annual interest rate (in decimal) = r
The number of times that interest is compounded per year = n
The time the money is invested for in years = t
After 15 years, A = 6P.
Substituting these values into the formula for compound interest:
6P = P(1 + r/1)
6 = (1 + r)
We take the 15th root of both sides to get:
1 + r = 6
1 + r = 1.1225
r = 0.1225
0.1225 = 12.25% (0.1225 x 100)
r = 12.25%
Thus, the rate of interest per annum at which the sum of money will become 6 times itself in 15 years compounded annually is 12.25%.
Complete Question:
At what rate of interest of CI (Compound Interest) will a sum of money become 6 times the original value in 15 years compounded annually?