#please people i need your help over this question#
How much should George be loaned by the bank that offers an interest of 23% if he returned an interest of sh 1,311,000 after 3 years?
To determine how much George should be loaned by the bank, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount accumulated after time t, including both the principal and interest
P = the principal (the initial loan amount)
r = the annual interest rate (written as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, we are given the interest (A), the interest rate (r), and the time (t) in years. We need to solve for the principal (P).
Let's plug in the values we know:
A = sh 1,311,000 (the accumulated amount after 3 years)
r = 23% = 0.23 (expressed as a decimal)
n = 1 (since interest is compounded annually)
t = 3 years
Using these values, the formula becomes:
sh 1,311,000 = P(1 + 0.23/1)^(1*3)
Now, let's solve for P:
sh 1,311,000 = P(1 + 0.23)^3
sh 1,311,000 = P(1.23)^3
sh 1,311,000 = P(1.73205)
To isolate P, we can divide both sides of the equation by 1.73205:
sh 1,311,000 / 1.73205 = P
Calculating this, we find:
P ≈ sh 757,027.39
Therefore, George should be loaned approximately sh 757,027.39 by the bank.