Mr. Ismail invested sh. 36,000 in the bank which gives an interest of 20% per year. After how long will he get sh. 43,200?
#please people help me this question how to arrive to final answer. Also i need to know if sh. 43,200 is either the total amount of money (P+I) or the interest given by the bank with reasons.
Thank you for your cooperation#
Interest = principal times rate times time
43,000 = 36,000 * 0.2 * t
Solve for t.
This approach gives the answer in fraction, but the answer from book is 1 year.
To find out how long it will take for Mr. Ismail to get sh. 43,200, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (sh. 43,200 in this case)
P = the principal amount (sh. 36,000 in this case)
r = the annual interest rate (20%, which can be written as 0.20)
n = the number of times interest is compounded per year (this information is not given, so we will assume it is compounded annually)
t = the time in years (we need to find this)
Now we can substitute the given values into the formula:
43,200 = 36,000(1 + 0.20/1)^(1t)
Simplifying:
43,200/36,000 = (1.20)^t
Dividing both sides by 36,000:
1.2 = 1.20^t
To solve for t, we can take the natural logarithm (ln) of both sides:
ln(1.2) = ln(1.20^t)
Using logarithm properties, we can bring down the exponent:
ln(1.2) = t * ln(1.20)
Now we can solve for t by dividing both sides by ln(1.20):
t = ln(1.2) / ln(1.20)
Using a scientific calculator or software, we can calculate this value:
t ≈ 3.221
Therefore, it will take approximately 3.221 years for Mr. Ismail to get sh. 43,200.
Regarding your second question, sh. 43,200 represents the final amount of money (principal + interest).
To find out how long it will take Mr. Ismail to get sh. 43,200, we need to calculate the amount of interest earned by the investment and add it to the initial investment.
The formula to calculate the amount of interest earned can be written as:
Interest = Principal * Rate * Time
Where:
- Principal is the initial investment (sh. 36,000)
- Rate is the interest rate per year (20% or 0.20)
- Time is the number of years
To find the time (number of years), we can rearrange the formula as follows:
Time = Interest / (Principal * Rate)
In this case, the total amount of money (sh. 43,200) is the sum of the initial investment (sh. 36,000) and the interest earned. So, sh. 43,200 represents the total amount of money (P + I), not just the interest.
Let's now calculate the time it will take for Mr. Ismail to reach sh. 43,200:
Interest = sh. 43,200 - sh. 36,000 = sh. 7,200
Time = sh. 7,200 / (sh. 36,000 * 0.20) = sh. 7,200 / sh. 7,200 = 1 year
Therefore, it will take Mr. Ismail 1 year to accumulate sh. 43,200 in the bank.