When the rate of interest in the bank is increased from 5% to 6% per annum,Gerald deposits Tsh 12,000 more into his account.If annum interest now received by him is Tsh 1100 more than that before,find his original deposit.**please anyone to help me with the solution***
If the initial deposit was x, then compare the interest:
.06(x+12000) = .05x + 1100
x = 38000
how about the time because from interest,I = prt
To solve this problem, we need to set up an equation based on the given information.
Let x be Gerald's original deposit.
Given:
Interest rate before = 5% per annum
Interest rate after = 6% per annum
Additional deposit = Tsh 12,000
Additional interest received = Tsh 1,100
Now, let's break down the problem step by step:
1. Calculate the interest received before:
Interest received before = (x * 5%) / 100
2. Calculate the interest received after:
Interest received after = [(x + 12,000) * 6%] / 100
3. Set up an equation using the given information:
Interest received after - Interest received before = Tsh 1,100
[(x + 12,000) * 6%] / 100 - (x * 5%) / 100 = 1,100
4. Simplify the equation:
[(x + 12,000) * 6% - x * 5%] / 100 = 1,100
Multiply both sides of the equation by 100 to remove the fraction:
(6(x + 12,000) - 5x) / 100 = 1,100
Multiply through by 100 to eliminate the fraction:
6(x + 12,000) - 5x = 1,100 * 100
Distribute and simplify:
6x + 72,000 - 5x = 110,000
x + 72,000 = 110,000
5. Solve for x:
x = 110,000 - 72,000
x = 38,000
Therefore, Gerald's original deposit was Tsh 38,000.